New Publications Offered by the AMS

836 NOTICES OF THE AMS VOLUME 51, NUMBER 7

New PublicationsOffered by the AMS

Algebra and AlgebraicGeometry

Galois Theory, Hopf Algebras, and SemiabelianCategoriesGeorge Janelidze, RazmadzeMathematical Institute of theGeorgian Academy of Sciences,Tbilisi, Republic of Georgia,Bodo Pareigis, University ofMunich, Germany, and Walter Tholen, York University, Toronto, ON, Canada, Editors

This volume is based on talks given at the Workshop on Cate-gorical Structures for Descent and Galois Theory, HopfAlgebras, and Semiabelian Categories held at The Fields Insti-tute for Research in Mathematical Sciences (Toronto, ON,Canada). The meeting brought together researchers working inthese interrelated areas.

This collection of survey and research papers gives an up-to-date account of the many current connections among Galoistheories, Hopf algebras, and semiabelian categories. The bookfeatures articles by leading researchers on a wide range ofthemes, specifically, abstract Galois theory, Hopf algebras, andcategorical structures, in particular quantum categories andhigher-dimensional structures.

Articles are suitable for graduate students and researchers,specifically those interested in Galois theory and Hopf alge-bras and their categorical unification.

Contents: M. Barr, Algebraic cohomology: The early days;F. Borceux, A survey of semi-abelian categories; D. Bourn,Commutator theory in regular Mal’cev categories; D. Bournand M. Gran, Categorical aspects of modularity; R. Brown,Crossed complexes and homotopy groupoids as non commu-tative tools for higher dimensional local-to-global problems;M. Bunge, Galois groupoids and covering morphisms in topostheory; S. Caenepeel, Galois corings from the descent theorypoint of view; B. Day and R. Street, Quantum categories, star

autonomy, and quantum groupoids; J. W. Duskin,R. W. Kieboom, and E. M. Vitale, Morphisms of 2-groupoidsand low-dimensional cohomology of crossed modules;M. Gran, Applications of categorical Galois theory in universalalgebra; C. Hermida, Fibrations for abstract multicategories;J. Huebschmann, Lie-Rinehart algebras, descent, and quantiza-tion; P. Johnstone, A note on the semiabelian variety ofHeyting semilattices; G. M. Kelly and S. Lack, Monoidal func-tors generated by adjunctions, with applications to transportof structure; M. Khalkhali and B. Rangipour, On the cyclichomology of Hopf crossed products; G. Lukács, On sequen-tially h-complete groups; J. L. MacDonald, Embeddings ofalgebras; A. R. Magid, Universal covers and category theory inpolynomial and differential Galois theory; N. Martins-Ferreira,Weak categories in additive 2-categories with kernels; T. Palm,Dendrotopic sets; A. H. Roque, On factorization systems andadmissible Galois structures; P. Schauenburg, Hopf-Galois andbi-Galois extensions; J. D. H. Smith, Extension theory inMal’tsev varieties; L. Sousa, On projective generators relativeto coreflective classes; J. J. Xarez, The monotone-light factor-ization for categories via preorders; J. J. Xarez, Separablemorphisms of categories via preordered sets; S. Yamagami,Frobenius algebras in tensor categories and bimodule exten-sions.

Fields Institute Communications, Volume 43

August 2004, 570 pages, Hardcover, ISBN 0-8218-3290-5, LC 2004050271, 2000 Mathematics Subject Classification:08Bxx, 12Hxx, 13Bxx, 14Lxx, 16Dxx, 17Bxx, 18–XX, 19Dxx,22Axx, All AMS members $103, List $129, Order code FIC/43N

Analysis

In the Tradition ofAhlfors and Bers, IIIWilliam Abikoff and Andrew Haas, University ofConnecticut, Storrs, Editors

This proceedings volume reflects the2001 Ahlfors-Bers Colloquium held atthe University of Connecticut (Storrs).This conference began nearly a halfcentury ago with a tradition based onprofound mathematics, wide-ranging

FIELDS INSTITUTE

COMMUNICATIONS

THE FIELDS INSTITUTE FOR RESEARCH IN MATHEMATICAL SCIENCES

Galois Theory, Hopf Algebras, and

Semiabelian CategoriesGeorge Janelidze

Bodo PareigisWalter Tholen

Editors

American Mathematical Society

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In the Tradition of Ahlfors and Bers, III

William AbikoffAndrew Haas

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AUGUST 2004 NOTICES OF THE AMS 837

New Publications Offered by the AMS

interests, personal involvement, and scholarship. Once led byLipman Bers and Lars Ahlfors, the core of this traditionunfolded around geometric function theory.

Talks at the colloquium were devoted to various aspects ofcomplex analysis, including Teichmüller spaces, quasicon-formal mappings, and geometric function theory. The book issuitable for graduate students and researchers interested incomplex analysis.

Contents: W. Abikoff, C. J. Earle, and S. Mitra, Barycentricextensions of monotone maps of the circle; H. Akiyoshi,H. Miyachi, and M. Sakuma, A refinement of McShane’s iden-tity for quasifuchsian punctured torus groups; C. J. Bishop,An explicit constant for Sullivan’s convex hull theorem; G. Ble,A. Douady, and C. Henriksen, Round annuli; M. Bonk,J. Heinonen, and E. Saksman, The quasiconformal Jacobianproblem; M. Bridgeman, Random geodesics; R. D. Canary,Pushing the boundary; R. Chamanara, Affine automorphismgroups of surfaces of infinite type; G. Cui, F. P. Gardiner, andY. Jiang, Scaling functions for degree 2 circle endomorphisms;E. de Faria, F. P. Gardiner, and W. J. Harvey, Thompson’sgroup as a Teichmüller mapping class group; C. J. Earle,F. P. Gardiner, and N. Lakic, Asymptotic Teichmüller space,part II: The metric structure; A. Eremenko, Geometric theoryof meromorphic functions; H. M. Farkas and I. Kra, Identitiesin the theory of theta constants; E. Fujikawa, Modular groupsacting on infinite dimensional Teichmüller spaces; D. M. Gallo,Some infinitesimal properties of the grafting map;P. M. Gauthier and M. R. Pouryayevali, Failure of Landau’stheorem for quasiconformal mappings of the disc; J. Holt,Bumping and self-bumping of deformation spaces; J. Hu,Earthquake measure and cross-ratio distortion; H. A. Masurand Y. N. Minsky, Quasiconvexity in the curve complex;K. Matsuzaki, Indecomposable continua and the limit sets ofKleinian groups; I. Petrovic, A Teichmüller model for perioddoubling.

Contemporary Mathematics, Volume 355

July 2004, 351 pages, Softcover, ISBN 0-8218-3607-2, LC 2004049691, 2000 Mathematics Subject Classification:30–06; 30C62, 30F30, 30F40, 30F60, 32G15, 57M50, All AMSmembers $71, List $89, Order code CONM/355N

Applications

Recent Advances inthe Theory andApplications of MassTransportM. C. Carvalho, GeorgiaInstitute of Technology,Atlanta, and University ofLisbon, and J. F. Rodrigues,University of Lisbon, Editors

This volume is the result of the Summer School on MassTransportation Methods in Kinetic Theory and Hydrodynamicsheld in Ponta Delgada (Azores, Portugal). It contains bothsurvey and research articles on methods of optimal masstransport and applications in physics. Among the many impor-

tant contributors are L. Caffarelli, M. Loss, and C. Villani. Thematerial is suitable for graduate students and research mathe-maticians interested in methods of mass transport.

This item will also be of interest to those working in differentialequations.

Contents: J.-D. Benamou, Y. Brenier, and K. Guittet, Numer-ical analysis of a multi-phasic mass transport problem;Y. Brenier, Extension of the Monge-Kantorovich theory to clas-sical electrodynamics; L. A. Caffarelli, The Monge Ampereequation and optimal transportation; E. Carlen and M. Loss,Logarithmic Sobolev inequalities and spectral gaps;D. Cordero-Erausquin, Non-smooth differential properties ofoptimal transport; D. Cordero-Erausquin, W. Gangbo, andC. Houdré, Inequalities for generalized entropy and optimaltransportation; C. Villani, Trend to equilibrium for dissipativeequations, functional inequalities and mass transportation.

Contemporary Mathematics, Volume 353

July 2004, 109 pages, Softcover, ISBN 0-8218-3278-6, LC 2004047695, 2000 Mathematics Subject Classification:35J60, 58J20, 49Q20, 35Q35, All AMS members $31, List $39, Order code CONM/353NFor Classroom Use

ComputationalComplexity TheorySteven Rudich, CarnegieMellon University, Pittsburgh,PA, and Avi Wigderson,Institute for Advanced Study,Princeton, NJ, Editors

Computational complexity theory is amajor research area in mathematicsand computer science, the goal of

which is to set the formal mathematical foundations for effi-cient computation.

There has been significant development in the nature andscope of the field in the last thirty years. It has evolved toencompass a broad variety of computational tasks by adiverse set of computational models, such as randomized,interactive, distributed, and parallel computations. Thesemodels can include many computers, which may behave coop-eratively or adversarially.

Each summer the IAS/Park City Mathematics Institute Grad-uate Summer School gathers some of the best researchers andeducators in the field to present diverse sets of lectures. Thisvolume presents three weeks of lectures given at the SummerSchool on Computational Complexity Theory. Topics are struc-tured as follows:

Week One: Complexity Theory: From Gödel to Feynman. Thissection of the book gives a general introduction to the field,with the main set of lectures describing basic models, tech-niques, results, and open problems.

Week Two: Lower Bounds on Concrete Models. Topicsdiscussed in this section include communication and circuitcomplexity, arithmetic and algebraic complexity, and proofcomplexity.

Week Three: Randomness in Computation. Lectures aredevoted to different notions of pseudorandomness, interactive

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Recent Advances in the Theory and Applications of Mass Transport

M. C. CarvalhoJ. F. Rodrigues

Editors

IAS/PARK CITYMATHEMATICS SERIES

Volume 10

ComputationalComplexity

TheorySteven RudichAvi Wigderson

Editors

American Mathematical SocietyInstitute for Advanced Study

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proof systems and zero knowledge, and probabilisticallycheckable proofs (PCPs).

The volume is recommended for independent study and issuitable for graduate students and researchers interested incomputational complexity.

This item will also be of interest to those working in logic andfoundations.

Members of the Mathematical Association of America (MAA) and theNational Council of Teachers of Mathematics (NCTM) receive a 20%discount from list price.

Contents: Introduction; Week One. Complexity Theory: FromGödel to Feynman: Steven Rudich, Complexity Theory: FromGödel to Feynman: History and basic concepts; Resources,reductions and P vs. NP; Probabilistic and quantum computa-tion; Complexity classes; Space complexity and circuitcomplexity; Oracles and the polynomial time hierarchy; Circuitlower bounds; “Natural” proofs of lower bounds; Bibliography;Avi Wigderson, Average Case Complexity: Average casecomplexity; Bibliography; Sanjeev Arora, Exploring Complexitythrough Reductions: Introduction; PCP theorem and hardnessof computing approximate solutions; Which problems havestrongly exponential complexity?; Toda’s theorem: PH ⊆ P#P ;Bibliography; Ran Raz, Quantum Computation: Introduction;Bipartite quantum systems; Quantum circuits and Shor’sfactoring algorithm; Bibliography; Week Two. Lower Bounds:Ran Raz, Circuit and Communication Complexity: Communica-tion complexity; Lower bounds for probabilisticcommunication complexity; Communication complexity andcircuit depth; Lower bound for directed st-connectivity; Lowerbound for FORK (continued); Bibliography; Paul Beame, ProofComplexity: An introduction to proof complexity; Lowerbounds in proof complexity; Automatizability and interpola-tion; The restriction method; Other research and openproblems; Bibliography; Week Three. Randomness in Computa-tion: Preface; Oded Goldreich, Pseudorandomness–Part I:Preface; Computational indistinguishability; Pseudorandomgenerators; Pseudorandom functions and concluding remarks;Appendix; Bibliography; Luca Trevisan,Pseudorandomness–Part II: Introduction; Deterministic simula-tion of randomized algorithms; The Nisan-Wigdersongenerator; Analysis of the Nisan-Wigderson generator;Randomness extractors; Bibliography; Salil Vadhan, Proba-bilistic Proof Systems–Part I: Interactive proofs; Zero-knowledgeproofs; Suggestions for further reading; Bibliography; MadhuSudan, Probabilistically Checkable Proofs: Introduction to PCPs;NP-hardness of PCS; A couple of digressions; Proof composi-tion and the PCP theorem; Bibliography.

IAS/Park City Mathematics Series, Volume 10

September 2004, 389 pages, Hardcover, ISBN 0-8218-2872-X,2000 Mathematics Subject Classification: 68Qxx; 03D15, AllAMS members $55, List $69, Order code PCMS/10N

Logic and Foundations

The Stationary TowerNotes on a Course by W. Hugh WoodinPaul B. Larson, MiamiUniversity, Oxford, OH

The stationary tower is an importantmethod in modern set theory, invented

by Hugh Woodin in the 1980s. It is a means of constructinggeneric elementary embeddings and can be applied to producea variety of useful forcing effects.

Hugh Woodin is a leading figure in modern set theory, havingmade many deep and lasting contributions to the field, inparticular to descriptive set theory and large cardinals. Thisbook is the first detailed treatment of his method of thestationary tower that is generally accessible to graduatestudents in mathematical logic. By giving complete proofs ofall the main theorems and discussing them in context, it isintended that the book will become the standard reference onthe stationary tower and its applications to descriptive settheory.

The first two chapters are taken from a graduate courseWoodin taught at Berkeley. The concluding theorem in thecourse was that large cardinals imply that all sets of reals inthe smallest model of set theory (without choice) containingthe reals are Lebesgue measurable. Additional sections includea proof (using the stationary tower) of Woodin’s theorem that,with large cardinals, the Continuum Hypothesis settles allquestions of the same complexity as well as some of Woodin’sapplications of the stationary tower to the studies of absolute-ness and determinacy.

The book is suitable for a graduate course that assumes somefamiliarity with forcing, constructibility, and ultrapowers. It isalso recommended for researchers interested in logic, settheory, and forcing.

Contents: Elementary embeddings; The stationary tower;Applications; Appendix: Forcing prerequisites; Bibliography;Index.

University Lecture Series, Volume 32

August 2004, 132 pages, Softcover, ISBN 0-8218-3604-8, LC 2004047666, 2000 Mathematics Subject Classification:03E40, 03E15, 03E35, 03E55, 03E60, All AMS members $23,List $29, Order code ULECT/32N


LECTUREUniversity

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The Stationary TowerNotes on a Course

by W. Hugh Woodin

Paul B. Larson

For Classroom Use



Mathematical Physics

Supersymmetry for Mathematicians:An IntroductionV. S. Varadarajan, University ofCalifornia, Los Angeles

Supersymmetry has been studied bytheoretical physicists since the early1970s. Nowadays, because of itsnovelty and significance—in bothmathematics and physics—the issues

it raises attract the interest of mathematicians.

Written by the well-known mathematician, V. S. Varadarajan,this book presents a cogent and self-contained exposition ofthe foundations of supersymmetry for the mathematically-minded reader. It begins with a brief introduction to thephysical foundations of the theory, in particular, to the classi-fication of relativistic particles and their wave equations, suchas those of Dirac and Weyl. It then continues with the develop-ment of the theory of supermanifolds, stressing the analogywith the Grothendieck theory of schemes. Here, Varadarajandevelops all the super linear algebra needed for the book andestablishes the basic theorems: differential and integralcalculus in supermanifolds, Frobenius theorem, foundations ofthe theory of super Lie groups, and so on. A special feature isthe in-depth treatment of the theory of spinors in all dimen-sions and signatures, which is the basis of all supergeometrydevelopments in both physics and mathematics, especially inquantum field theory and supergravity.

The material is suitable for graduate students and mathemati-cians interested in the mathematical theory of supersymmetry.The book is recommended for independent study.

Titles in this series are copublished with the Courant Institute of Math-ematical Sciences at New York University.

Contents: Introduction; The concept of a supermanifold; Superlinear algebra; Elementary theory of supermanifolds; Cliffordalgebras, spin groups, and spin representations; Fine structureof spin modules; Superspacetimes and super Poincaré groups.

Courant Lecture Notes, Volume 11

August 2004, 300 pages, Softcover, ISBN 0-8218-3574-2, LC 2004052349, 2000 Mathematics Subject Classification:58A50, 58C50, 17B70, 22E99; 14A22, 14M30, 32C11, All AMS members $31, List $39, Order code CLN/11N

More PublicationsAvailable from the AMS

Algebra and AlgebraicGeometry

Séminaire BourbakiVolume 2001/2002Exposés 894/908As in the preceding volumes of thisseminar, one finds here fifteen surveylectures on topics of current interest:three lectures on algebraic geometry,two on dynamical systems, one onactions of finite groups, one on combi-natorics and algebraic geometry, oneon theoretical computer science, one

on p-adic monodromy, one on Iwasawa algebras, one on theKato conjecture, one on renormalization and Feynmandiagrams, one on dualities in string theory, one on thegeometric Langlands correspondence, and one on “dessinsd’enfants”.

The book is suitable for graduate students and research math-ematicians interested in recent progress in algebraic geometry,number theory, differential equations, mathematical physics,discrete mathematics, combinatorics, and applications tocomputer science.

This item will also be of interest to those working in numbertheory.

A publication of the Société Mathématique de France, Marseilles (SMF),distributed by the AMS in the U.S., Canada, and Mexico. Orders fromother countries should be sent to the SMF. Members of the SMF receivea 30% discount from list.

Contents: Novembre 2001: A. Adem, Finite group actions onacyclic 2-complexes; B. Chazelle, The PCP theorem; J. Coates,Iwasawa algebras and arithmetic; P. Colmez, Les conjecturesde monodromie p-adiques; C. Procesi, On the n!-conjecture;Mars 2002: D. Bennequin, Dualités de champs et de cordes;L. Boutet de Monvel, Algèbre de Hopf des diagrammes deFeynman, renormalisation et factorisation de Wiener-Hopf;F. Loeser, Cobordisme des variétés algébriques; Y. Meyer, Laconjecture de Kato; M. Rapoport, On the Newton stratification;Juin 2002: C. Bonatti, Dynamiques génériques: hyperbolicité ettransitivité; O. Debarre, Variétés rationnellement connexes;G. Laumon, Travaux de Frenkel, Gaitsgory et Vilonen sur lacorrespondance de Drinfeld-Langlands; J. Oesterlé, Dessinsd’enfants; R. Pérez-Marco, KAM techniques in PDE.

Astérisque, Number 290

April 2004, 234 pages, Softcover, ISBN 2-85629-149-X, 2000Mathematics Subject Classification: 00B25, Individual member$74, List $82, Order code AST/290N

C O U R A N T

Supersymmetry for Mathematicians: An Introduction

V . S . V A R A D A R A J A N LECTURE

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SÉMINAIRE BOURBAKI

VOLUME 2001/2002

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For Classroom Use


More Publications Available from the AMS

Analysis

Complex Analysis inSeveral VariablesMemorial Conference ofKiyoshi Oka’s CentennialBirthday, Kyoto/Nara2001Kimio Miyajima, KagoshimaUniversity, Japan, Mikio Furushima, KumamotoUniversity, Japan, Hideaki

Kazama, Kyushu University, Fukuoka, Japan, AkioKodama, Kanazawa University, Japan, JunjiroNoguchi, University of Tokyo, Japan, TakeoOhsawa, Nagoya University, Japan, Hajime Tsuji,Sophia University, Tokyo, Japan, and TetsuoUeda, Kyoto University, Japan, Editors

This volume resulted from a conference held at Kyoto Univer-sity and Nara Women’s University (Japan) in commemorationof the late Professor Kiyoshi Oka, one of the most famousJapanese mathematicians. Included are 34 research and surveypapers contributed by the invited lecturers and a letter writtenfor the occasion by H. Cartan.

Among the leading mathematicians who contributed to thevolume are E. Bedford, S. Kobayashi, J. J. Kohn, and M. Kuran-ishi. Topics discussed include pseudoconvex domains, ∂analysis (including L2 theory), the Bergman kernel, valuedistribution theory, hyperbolic manifolds, dynamical systems,infinite dimensional complex analysis, algebraic analysis, CRstructure, singularity theory, algebraic geometry, and others.

The book is suitable for advanced graduate students andresearch mathematicians interested in complex analysis, alge-braic geometry, and complex geometry.

Published for the Mathematical Society of Japan by Kinokuniya, Tokyo,and distributed worldwide, except in Japan, by the AMS.

Contents: Part I: Photos of Kiyoshi Oka; Oka, Kiyoshi; Memo-rial conference of Kiyoshi Oka’s centennial birthday oncomplex analysis in several variables, Kyoto/Nara 2001;Message from Professor Henri Cartan; Part II: T. Nishino,Mathematics of Professor Oka—a landscape in his mind;Y. Aihara, Uniqueness problem for meromorphic mappingsunder conditions on the preimages of divisors; T. Akahori, Onthe middle dimension cohomology of A1 singularity; T. Aoki,T. Kawai, and Y. Takei, The exact steepest descent method—anew steepest descent method based on the exact WKBanalysis; E. Bedford, Excursions of a complex analyst into therealm of dynamical systems; J. El Goul, Demailly’s 2-jet nega-tivity of certain hyperbolic fibrations; J. E. Fornæss, Short Ck ;H. Fujimoto, Some constructions of hyperbolic hypersurfacesin Pn(C) ; K. Hirachi, A link between the asymptotic expan-sions of the Bergman kernel and the Szegö kernel; A. Iordan,On the non-existence of smooth Levi-flat hypersurfaces inCPn; S.-J. Kan, Recent development on Grauert domains; K.-T. Kim, Analytic polyhedra with non-compact automor-phism group; S. Kobayashi, Problems related to hyperbolicity

of almost complex structures; J. J. Kohn, Ideals of multipliers;G. Komatsu, The Bergman kernel of Hartogs domains andtransformation laws for Sobolev-Bergman kernels; M. Kuran-ishi, An approach to the Cartan geometry II: CR manifolds;L. Lempert, The ∂ equation in N variables, as N varies;K. Matsumoto, Levi form of logarithmic distance to complexsubmanifolds and its application to developability;Y. Miyaoka, Numerical characterisations of hyperquadrics;S. Mori, Meromorphic mappings and deficiencies; J. Noguchi,Intersection multiplicities of holomorphic and algebraic curveswith divisors; T. Ohsawa, Generalization of a precise L2 divi-sion theorem; M. Passare, Amoebas, convexity and the volumeof integer polytopes; R. M. Range, On the decomposition ofholomorphic functions by integrals and the local CR extensiontheorem; O. Riemenschneider, The monodromy covering ofthe versal deformation of cyclic quotient surface singularities;G. Schumacher, Moduli as algebraic spaces; S. Shimizu,Prolongation of holomorphic vector fields on a tube domainand its applications; M. Shirosaki, Hypersurfaces and unique-ness of holomorphic mappings; S. Takayama, Seshadriconstants and a criterion for bigness of pseudo-effective linebundles; H. Tsuji, Subadjunction theorem; T. Ueda, Fixedpoints of polynomial automorphisms of Cn; K. Yamanoi, OnNevanlinna theory for holomorphic curves in abelian varieties;S.-T. Yau, Numerical characterization for affine varieties be acone over nonsingular projective varieties; K.-I. Yoshikawa,Nikulin’s K3 surfaces, adiabatic limit of equivariant analytictorsion, and the Borcherds Φ-function.

Advanced Studies in Pure Mathematics, Volume 42

June 2004, 360 pages, Hardcover, ISBN 4-931469-27-2, 2000 Mathematics Subject Classification: 00B20; 32Axx, 32Exx,32Fxx, 32Hxx, 32Qxx, 32Sxx, 32Vxx, 32Wxx, 37Fxx, 14Cxx,14Jxx, 14Rxx, 58Jxx, All AMS members $74, List $92, Ordercode ASPM/42N

Number Theory

Variétés de Shimura, espaces de Rapoport-Zink etcorrespondances deLanglands localesLaurent Fargues, UniversitéParis/CNRS, Orsay, France,and Elena Mantovan,University of California,Berkeley

This volume contains two articles. Both deal with generaliza-tions of Michael Harris’ and Richard Taylor’s work on thecohomology of P.E.L. type Shimura varieties of signature(1, n− 1) and on the cohomology of Lubin-Tate spaces. Theyare based on the work of Robert Kottwitz on those varieties inthe general signature case, and on the work of MichaelRapoport and Thomas Zink on moduli spaces of p-divisiblegroups generalizing the one of Lubin-Tate and Drinfeld.

In the first article it is proved that the -adique étale coho-mology of some of those “supersingular” moduli spaces of

ADVANCED STUDIES IN PUREMATHEMATICS 42

Mathematical Society of Japan, Tokyo

Complex Analysis in Several Variables Memorial Conference of Kiyoshi Oka's Centennial Birthday Kyoto/Nara 2001

Kimio Miyajima, Mikio Furushima, Hideaki Kazama, Akio Kodama,Junjiro Noguchi, Takeo Ohsawa, Hajime Tsuji, and Tetsuo Ueda

291

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ASTÉRISQUE

SOCIÉTÉ MATHÉMATIQUE DE FRANCEPublié avec le concours du CENTRE NATIONAL DE LA RECHERCHE SCIENTIFIQUE

VARIETES DE SHIMURA, ESPACES DE RAPOPORT-ZINK ET CORRESPONDANCES DE

LANGLANDS LOCALES

Laurent FARGUES

Elena MANTOVAN


p-divisible groups realizes some cases of local Langlandscorrespondences. For this the author establishes a formulalinking the cohomology of those spaces to the one of the“supersingular” locus of a Shimura variety. Then he provesthat the supercuspidal part of the cohomology of those vari-eties is completely contained in the one of the “supersingular”locus.

The second article links the cohomology of a Newton stratumof the Shimura variety, for example the “supersingular”stratum, to the cohomology of the attached local moduli spaceof p-divisible groups and to the cohomology of some globalvarieties in positive characteristic named Igusa varieties thatgeneralize the classical Igusa curves attached to modularcurves.

The book is suitable for graduate students and research math-ematicians interested in number theory and algebraicgeometry.

This item will also be of interest to those working in algebraand algebraic geometry.

A publication of the Société Mathématique de France, Marseilles (SMF),distributed by the AMS in the U.S., Canada, and Mexico. Orders fromother countries should be sent to the SMF. Members of the SMF receivea 30% discount from list.

Contents: L. Fargues. Cohomologie des espaces de modules degroupes p-divisibles et correspondances de Langlands locales:Introduction; Variétés de Shimura de type P.E.L. non ramifiées;Espaces de Rapoport-Zink; Uniformisation des variétés deShimura de type P.E.L.; Une suite spectrale de Hochschild-Serrepour l’uniformisation de Rapoport-Zink; Formule de Lefschetzsur la fibre spéciale; Formule de Lefschetz sur la fibregénérique; Contribution de la cohomologie de la stratebasique; Application à la cohomologie des espaces Rapoport-Zink de type E.L. et P.E.L.; Appendices; Références; E. Mantovan. On Certain Unitary Shimura Varieties: Introduc-tion; Preliminaries; Igusa varieties; A system of covers of theNewton polygon strata; Group action on cohomology; Formallylifting to characteristic zero; Shimura varieties with levelstructure at p; The cohomology of Shimura varieties; Refer-ences.

Astérisque, Number 291

April 2004, 331 pages, Softcover, ISBN 2-85629-150-3, 2000 Mathematics Subject Classification: 11G18, 11Fxx, 14G35,14L05, 14G22, Individual member $86, List $95, Order codeAST/291N

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