Modern Birkhauser Classics

Many of the original research and survey monographs in pure and applied mathematics published by Birkhauser in recent decades have been groundbreaking and have come to be regarded as foun• dational to the subject. Through the MBC Series, a select number of these modern classics, entirely uncorrected, are being re-released in paperback (and as eBooks) to ensure that these treasures remain ac• cessible to new generations of students, scholars, and researchers. The Grothendieck Festschrift Volume II

A Collection of Articles Written in Honor of the 60th Birthday of Alexander Grothendieck

P. Cartier L. lUusie N.M. Katz G. Laumon Yu.I. Manin K.A. Ribet Editors

Reprint of the 1990 Edition

Birkhauser Boston • Basel • Berlin Luc lUusie Pierre Cartier Universite de Paris-Sud Institut des Hautes Etudes Scientifiques Departement de Mathematiques F-91440 Bures-sur-Yvette F-91405 Orsay France France

Gerard Laumon Nicholas M. Katz Universite de Paris-Sud Princeton University Departement de Math6matiques Department of Mathematics F-91405 Orsay Princeton, NJ 08544 France U.S.A.

Yuri I. Manin Kenneth A. Ribet Max-Planck Institut ftir Mathematik University of California D-53111 Bonn Department of Mathematics Germany Berkeley, CA 94720 U.S.A.

Originally published as Volume 87 in the series Progress in Mathematics

Cover design by Alex Gerasev.

Mathematics Subject Classification (2000): 00B15, 00B30, 01A60, 01A75 (primary); 11F37, 11F72, 11G05,11G40,11M41,11R29,11R34,11S23,11S31,11S37,12H05,13K05,13N10,14A99,14B15, 14C17, 14D05, 14E20, 14F05, 14F20, 14F30, 14F32, 14F35, 14F40, 14F99, 14G05, 14G10, 14H25, 14H40,14L05,14L15,14M10,14M15,17B10,17B67,18A99,18B40,18E30,18F20,20F34,20F36, 20L05, 22E35, 22E50, 32C15, 32C38, 32S50, 32S60, 57M07, 58G25. 58G26, 58J50, 58J52 (secondary)

Library of Congress Control Number: 2006936966

ISBN-10: 0-8176-4567-5 e-ISBN-10: 0-8176-4575-6 ISBN-13: 978-0-8176-4567-0 e-ISBN-13: 978-0-8176-4575-5

Printed on acid-free paper.

©2001 Birkhauser Boston BirkhdUSCr All rights reserved. This work may not be translated or copied in whole or in part without the writ• ten permission of the pubUsher (Birkhauser Boston, c/o Springer Science-f Business Media LLC, 233 Spnng Street, New York, NY 10013, USA), except for brief excerpts m connection with reviews or scholarly analysis. Use in connection with any form of information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter de• veloped is forbidden. The use in this publication of trade names, trademarks, service marks and similar terms, even if they are not identified as such, is not to be taken as an expression of opinion as to whether or not they are subject to proprietary rights.

987654321

www. birkhauser. com (IBT) p. Cartier L. Illusie N.M. Katz G. Laumon Y. Manin K.A. Ribet Editors

The Grothendieck Festschrift A Collection of Articles Written in Honor of the 60th Birthday of Alexander Grothendieck Volume II

1990 Birkhauser Boston • Basel • Berlin Pierre Cartier Luc Illusie Institut des Hautes Departement de Mathematiques Etudes Scientifiques Universite de Paris-Sud 91440 Bures-sur-Yvette Centre d'Orsay France 91405 Orsay Cedex France

Nicholas M. Katz Gerard Laumon Department of Mathematics Departement de Mathematiques Princeton University Universite de Paris-Sud Princeton, NJ 08544 Centre d'Orsay USA 91405 Orsay Cedex France

Yuri Manin Kenneth A. Ribet Steklov Institute Department of Mathematics Vavilova 42 University of California Moscow, 117966-GSPl Berkeley, CA 94720 USSR USA

Printed on acid-free paper.

© Birkhauser Boston, 1990. All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording or other• wise, without prior permission of the copyright owner. Permission to photocopy for internal or personal use, or the internal or personal use of specific clients, is granted by Birkhauser Boston, for libraries and other users registered with the Copyright Clearance Center (CCC), provided that the base fee of $0.00 per copy, plus $0 20 per page is paid directly to CCC, 21 Congress Street, Salem, MA 01970, U.S.A. Special requests should be ad• dressed directly to Birkhauser Boston, 675 Massachusetts Avenue, Cambridge, MA 02139, U.S.A. 3428-2/90 $0.00 + .20

ISBN 0-8176-3428-2 ISBN 0-8176-3429-0 Three-volume set ISBN 3-7643-3428-2 ISBN 3-7643-3429-0 Three-volume set

Printed and bound by Edwards Brothers, Inc., Ann Arbor, Michigan. Pnnted in the U.S.A.

987654321 CONTENTS

VOLUME II

Une nouvelle interpretation de la formule des traces de Selberg 1 PIERRE CARTIER et ANDRE VOROS

Jacobiennes generalisees globales relatives 69 C. CONTOU-CARRERE

Categories tannakiennes Ill P. DELIGNE

On The Adic Formalism 197 TORSTEN EKEDAHL

F-Isocrystals on Open Varieties: Results and Conjectures 219 GERD FALTINGS

Representations p-adiques des corps locaux 249 JEAN-MARC FONTAINE

Rectified Homotopical Depth and Grothendieck Conjectures 311 HELMUT A. HAMM and LE DUNG TRANG

Automorphisms of Pure Sphere Braid Groups and Galois Representations 353 YASUTAKA IHARA

Ordinarite des intersections completes generales 375 Luc ILLUSIE

V vi CONTENTS

Kazhdan-Lusztig Conjecture for a Symmetrizable Kac-Moody Lie Algebra 407 MASAKI KASHIWARA

Euler Systems 435 V.A. KOLYVAGIN

Descent for Transfer Factors 485 R. LANGLANDS and D. SHELSTAD

VOLUME I

Bibliographie D'Alexander Grothendieck

De L'Analyse Fonctionnelle aux Fondements de la Geometrie Algebrique JEAN DIEUDONNE

The presentation functor and the compactified Jacobian ALLEN B. ALTMAN and STEVEN L. KLEIMAN

Some Algebras Associated to Automorphisms of Elliptic Curves M. ARTIN, J. TATE, and M. VAN DEN BERGH

Cohomology of a Moduli Space of Vector Bundles V. BALAJI and C.S. SESHADRI

Sur les hypersurfaces dont les sections hyperplanes sont a module constant ARNAUD BEAUVILLE

Aomoto Dilogarithms, Mixed Hodge Structures, and Motivic Cohomology of Pairs of Triangles on the Plane A.A. BEILINSON, A.B. GONCHAROV, V.V. SCHECHTMAN, and A.N. VARCHENKO

Theorie de Dieudonne cristalline IIL theoremes d'equivalence et de pleine fidelite PIERRE BERTHELOT and WILLIAM MESSING

Complex Immersions and Arakelov Geometry JEAN-MICHEL BISMUT, HENRI GILLET, and CHRISTOPHE SOULE CONTENTS vii

L-Functions and Tamagawa Numbers of Motives SPENCER BLOCK and KAZUYA KATO

Bitorseurs et Cohomologie Non Abelienne LAWRENCE BREEN

Non-commutative Ruelle-SuUivan type currents JEAN-LUC BRYLINSKI

VOLUME III

Anneau de Grothendieck de la variete de drapeaux ALAIN LASCOUX

New Results on Weight-Two Motivic Cohomology S. LICHTENBAUM

Symmetric Spaces Over a Finite Field GEORGE LUSZTIG

Le theoreme de positivite de Tirregularite pour les 2);j^-modules ZOGHMAN MEBKHOUT

The Convergent Topos in Characteristic p ARTHUR OGUS

Finiteness Theorems and Hyperbolic Manifolds A.N. PARSHIN p-groupes et reduction semi-stable des courbes MICHEL RAYNAUD

Drawing Curves Over Number Fields G.B. SHABAT and V.A. VOEVODSKY

Sur les proprietes numeriques du dualisant relatif d'une surface arithmetique L. SZPIRO

Higher Algebraic K-Theory of Schemes and of Derived Categories R.W. THOMASON and THOMAS TROBAUGH viii CONTENTS

Solitons elliptiques A. TREIBICH and J.-L. VERDIER, with an Appendix by J. OESTERLE

Linear Simple Lie Algebras and Ranks of Operators Yu G. ZARHIN