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Progress in Mathematics Volume 269 Progress in Mathematics Volume 269 Series Editors Hyman Bass Joseph Oesterlé Alan Weinstein For other titles published in this series, go to http://www.springer.com/series/4848 Algebra, Arithmetic, and Geometry In Honor of Yu. I. Manin Volume I Yuri Tschinkel Yuri Zarhin Editors Birkhäuser Boston • Basel • Berlin Editors Yuri Tschinkel Yuri Zarhin New York University Pennsylvania State University Department of Mathematics Eberly College of Science New York, NY 10012-1185 Department of Mathematics [email protected] University Park, PA 16802 [email protected] ISBN 978-0-8176-4744-5 e-ISBN 978-0-8176-4745-2 DOI 10.1007/978-0-8176-4745-2 Springer New York Dordrecht Heidelberg London Library of Congress Control Number: 2009939499 c Springer Science+Business Media, LLC 2009 All rights reserved. This work may not be translated or copied in whole or in part without the written permission of the publisher (Birkhäuser Boston, c/o Springer Science+Business Media, LLC, 233 Spring Street, New York, NY 10013, USA), except for brief excerpts in connection with reviews or scholarly anal- ysis. 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 developed 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. Printed on acid-free paper Birkhäuser is part of Springer Science+Business Media (www.birkhauser.com) v Preface Yuri Ivanovich Manin has made outstanding contributions to algebra, algebraic geometry, number theory, algorithmic complexity, noncommutative geometry and mathematical physics. His numerous achievements include the proof of the functional analogue of the Mordell Conjecture, the theory of the Gauss–Manin connection, proof with V. Iskovskikh of the nonrationality of smooth quartic threefolds, the theory of p-adic automorphic functions, con- struction of instantons (jointly with V. Drinfeld, M. Atiyah and N. Hitchin), and the theory of quantum computations. We hope that the papers in this Festschrift, written in honor of Yu. I. Manin’s seventieth birthday, will indicate the great respect and admiration that his students, friends and colleagues throughout the world all have for him. June 2009 Courant Institute Yuri Tschinkel Penn State University Yuri Zarhin vii Contents Preface ........................................................ vii Curriculum Vitae: Yuri Ivanovich Manin ...................... xi List of Publications ............................................xvii Gerstenhaber and Batalin–Vilkovisky Structures on Lagrangian Intersections Kai Behrend and Barbara Fantechi ................................. 1 A Non-Archimedean Interpretation of the Weight Zero Subspaces of Limit Mixed Hodge Structures Vladimir G. Berkovich ............................................ 49 Analytic Curves in Algebraic Varieties over Number Fields Jean-Benoît Bost and Antoine Chambert-Loir ....................... 69 Riemann–Roch for Real Varieties Paul Bressler, Mikhail Kapranov, Boris Tsygan, and Eric Vasserot .....125 Universal KZB Equations: The Elliptic Case Damien Calaque, Benjamin Enriquez, and Pavel Etingof ..............165 Exact Category of Modules of Constant Jordan Type Jon F. Carlson and Eric M. Friedlander ............................267 Del Pezzo Moduli via Root Systems Elisabetta Colombo, Bert van Geemen, and Eduard Looijenga ..........291 The Weil Proof and the Geometry of the Adèles Class Space Alain Connes, Caterina Consani, and Matilde Marcolli ...............339 Elliptic Curves with Large Analytic Order of X(E) Andrzej Dąbrowski and Mariusz Wodzicki ...........................407 ix xContents p-adic Entropy and a p-adic Fuglede–Kadison Determinant Christopher Deninger .............................................423 Finite Subgroups of the Plane Cremona Group Igor V. Dolgachev and Vasily A. Iskovskikh..........................443 Lie Algebra Theory without Algebra Simon K. Donaldson .............................................549 Cycle Classes of the E-O Stratification on the Moduli of Abelian Varieties Torsten Ekedahl and Gerard van der Geer ...........................567 Experiments with General Cubic Surfaces Andreas-Stephan Elsenhans and Jörg Jahnel .........................637 Cluster Ensembles, Quantization and the Dilogarithm II: The Intertwiner V.V. Fock and A.B. Goncharov ....................................655 Operads Revisited Ezra Getzler .....................................................675 Curriculum Vitae Yuri Ivanovich Manin (updated May 30, 2009) Personal Born: February 16, 1937, Simferopol, Russia Married to Ksenia Glebovna Semenova Education M.S. (summa cum laude): Moscow State University, 1958 Ph.D. (Candidate of Phys. Math. Sci.): Steklov Institute, 1960 Doctor of Phys.-Math. Sci. (Habilitation): Steklov Institute, 1963 Employment Professor, Algebra Chair, Moscow University: 1965–1992 Principal Researcher, Steklov Institute, Academy of Sciences, Russia, Moscow: 1960–May 1993, since May 1993 Principal Researcher in absentia Professor, Department of Mathematics, MIT: 1992–1993 Scientific Member and Collegium Member, Max-Planck-Institut für Math., Bonn: May 1993–February 2005; Director: November 1995–February 2005; Managing Director: November 1999–October 2001; Professor Emeritus: March 2005–now Board of Trustees Professor, Northwestern University, Evanston: 2002–now Selected visiting appointments Pisa University, 1964 Montréal University, Aisenstadt Chair, 1988 IHES, Bures–sur–Yvette, France, 1967, 1989 xi xii Curriculum Vitae Collège de France, Paris, 1989 Berkeley University, Miller Professor, 1989 Harvard University, 1991 Columbia University, Eilenberg Chair, 1992 University of Antwerpen, International Francqui Chair, 1996–7 Collège de France, Paris, 2006 Service to the mathematical community Member, Shaw Prize in Mathematics Committee, 2008–2009 Member, Program Committee, European Congress of Mathematicians, Amsterdam, 2008 Member, Editorial Boards of two new Journals, founded in 2007: Non–Commutative Geometry; Algebra and Number Theory Member, Assessment Committee of the Academy Professorships Programme, Royal Netherlands Academy of Arts and Sciences, 2004–2005, 2005–2006, 2006–2007 Member, Selection Committee, King Faisal International Prize for Mathematics, 2005 Chair, Program Committee, International Congress of Mathematicians, Beijing, 2002 Chair, Fields Prize Committee, International Congress of Mathematicians, Berlin, 1998 Member, Board of the Moscow Mathematical Society (various years) Member, Program and Prize Committees of ICM and ECM (various years) Member, Editorial and Advisory Boards of Mathematical Sbornik, Uspekhi Math. Nauk, Inventiones Mathematicae, Duke Mathematical Journal, Functional Analysis and its Applications, Crelle’s Journal, Journal of Number Theory, Journal of Geometry and Physics, Advances of Mathematics, Inter- national Journal of Mathematics, American Journal of Mathematics et al. (various years) Member, International Benchmarking of US Research Field Study, Math. Panel, 1997 Member, Senior Jury of Institut Universitaire de France, 1999 Co–organizer of international conferences and workshops Mathematische Arbeitstagungen, Bonn, 1995, 1997 – 2007 Conformal Field Theory, Oberwolfach, 1996 Curriculum Vitae xiii Integrable systems, MPIM, Bonn, 1999 Non–Commutative Geometry, MPIM, Bonn, 1999 Frobenius Manifolds, MPIM, Bonn, 2002 Noncommutative Geometry and Number Theory, MPIM, Bonn, 2002, 2004 Dynamical Systems, MPIM, Bonn, 2004 Special session “Applications of Motives”, AMS annual meeting 2004, Evanston Geometry and Dynamics of Groups and Spaces, MPIM, 2006 Winter School and Workshop on Moduli Spaces, MPIM, 2008 Selected lectures Invited speaker at the ICM congresses: Moscow, 1966; Nice, 1970; Helsinki, 1978 (plenary); Berkeley, 1986; Kyoto, 1990; Madrid 2006 (special activity) Invited plenary speaker, European CM, Barcelona, 2000 Invited speaker at Bonn Arbeitstagungen: 1983, 1993 Rademacher Lecturer, University of Pennsylvania, 1989 Porter Lecturer, Rice University at Houston, 1989 Bowen Lecturer, Berkeley University, 1989 A. T. Brauer Lecturer, University of North Carolina, 1992 Leonardo da Vinci Lecturer, Milan University, 1992 Fermi Lecturer, Scuola Normale Superiore di Pisa, 1994 Schur Memorial Lecturer, Tel Aviv University, 1994 Regents’ Lecturer, University of California at Riverside, 1997 Coble lecturer, University of Illinois at Urbana–Champaigne, 1999 Chern Lecturer, University of California at Berkeley, 1999 Blythe Lecturer, University of Toronto, 2004 Hardy Lecturer, London Mathematical Society, 2006 Honors and awards Moscow Mathematical Society Award, 1963 Lenin Prize (Highest USSR National Prize), for work in Algebraic Geometry, 1967 Brouwer Gold Medal for work in Number Theory, Netherlands Royal Society and Mathematical Society, 1987 Frederic Esser Nemmers Prize in Mathematics, Northwestern University, Evanston, USA, 1994 Rolf Schock Prize in Mathematics of the Swedish Royal Academy of Sciences, Sweden, 1999 xiv Curriculum Vitae King Faisal International Prize for Mathematics, Saudi Arabia, 2002 Georg Cantor Medal of the German Mathematical Society, 2002 Order Pour le Mérite, Germany, 2007 Great Cross of Merit with Star, Germany, 2008 Elected Membership in Scientific Academies Corresponding Member, Academy of Sciences, Russia, 1990 Foreign
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