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Motives, Volume 55.2
http://dx.doi.org/10.1090/pspum/055.2 Recent Titles in This Series 55 Uwe Jannsen, Steven Kleiman, and Jean-Pierre Serre, editors, Motives (University of Washington, Seattle, July/August 1991) 54 Robert Greene and S. T. Yau, editors, Differential geometry (University of California, Los Angeles, July 1990) 53 James A. Carlson, C. Herbert Clemens, and David R. Morrison, editors, Complex geometry and Lie theory (Sundance, Utah, May 1989) 52 Eric Bedford, John P. D'Angelo, Robert £. Greene, and Steven G. Krantz, editors, Several complex variables and complex geometry (University of California, Santa Cruz, July 1989) 51 William B. Arveson and Ronald G. Douglas, editors, Operator theory/operator algebras and applications (University of New Hampshire, July 1988) 50 James Glimm, John Impagliazzo, and Isadore Singer, editors, The legacy of John von Neumann (Hofstra University, Hempstead, New York, May/June 1988) 49 Robert C. Gunning and Leon Ehrenpreis, editors, Theta functions - Bowdoin 1987 (Bowdoin College, Brunswick, Maine, July 1987) 48 R. O. Wells, Jr., editor, The mathematical heritage of Hermann Weyl (Duke University, Durham, May 1987) 47 Paul Fong, editor, The Areata conference on representations of finite groups (Humboldt State University, Areata, California, July 1986) 46 Spencer J. Bloch, editor, Algebraic geometry - Bowdoin 1985 (Bowdoin College, Brunswick, Maine, July 1985) 45 Felix E. Browder, editor, Nonlinear functional analysis and its applications (University of California, Berkeley, July 1983) 44 William K. Allard and Frederick J. Almgren, Jr., editors, Geometric measure theory and the calculus of variations (Humboldt State University, Areata, California, July/August 1984) 43 Francois Treves, editor, Pseudodifferential operators and applications (University of Notre Dame, Notre Dame, Indiana, April 1984) 42 Anil Nerode and Richard A. -
Motives: an Introductory Survey for Physicists
MOTIVES: AN INTRODUCTORY SURVEY FOR PHYSICISTS ABHIJNAN REJ (WITH AN APPENDIX BY MATILDE MARCOLLI) Abstract. We survey certain accessible aspects of Grothendieck's theory of motives in arith- metic algebraic geometry for mathematical physicists, focussing on areas that have recently found applications in quantum field theory. An appendix (by Matilde Marcolli) sketches further connections between motivic theory and theoretical physics. post hoc, ergo ante hoc { Umberto Eco, Interpretation and overinterpretation Contents 1. Introduction 1 2. The Grothendieck ring 2 3. The Tannakian formalism 6 4. Weil cohomology 12 5. Classical motives 15 6. Mixed motives 18 7. Motivic measures and zeta functions 22 8. Appendix: Motivic ideas in physics (by M.Marcolli) 24 References 29 1. Introduction This survey paper is based on lectures given by the author at Boston University, the Max Planck Institute in Bonn, at Durham university and at the Indian Statistical Institute and the SN Bose National Center for the Basic Sciences in Kolkata and the Indian Institute of Technology in Mumbai. The purpose of these introductory notes are to familiarize an audience of physicists with some of the algebraic and algebro-geometric background upon which Grothendieck's theory of motives of algebraic varieties relies. There have been many recent developments in the interactions between high energy physics and motives, mostly within the framework of perturbative quantum field theory and the evaluation of Feynman diagrams as periods of algebraic varieties, though motives are beginning to play an important role in other branched of theoretical physics, such as string theory, especially through the recent interactions with the Langlands program, and through the theory of BPS states. -
Notices of the American Mathematical Society
Calendar of AMS Meetings and Conferences This calendar lists all meetings and conferences approved prior to the date this issue insofar as is possible. Instructions for submission of abstracts can be found in the went to press. The summer and annual meetings are joint meetings with the Mathe January 1993 issue of the Notices on page 46. Abstracts of papers to be presented at matical Association of America. the meeting must be received at the headquarters of the Society in Providence, Rhode Abstracts of papers presented at a meeting of the Society are published in the Island. on or before the deadline given below for the meeting. Note that the deadline for journal Abstracts of papers presented to the American Mathematical Society in the abstracts for consideration for presentation at special sessions is usually three weeks issue corresponding to that of the Notices which contains the program of the meeting, earlier than that specified below. Meetings Abstract Program Meeting# Date Place Deadline Issue 893 June 16-18, 1994 Eugene, Oregon Expired May-June 894 August 15-17, 1994 (96th Summer Meeting) Minneapolis, Minnesota May 17 July-August 895 * October 28-29, 1994 Stillwater, Oklahoma August 3 October 896 * November 11-13, 1994 Richmond, Virginia August 3 October 897 January 4-7, 1995 (101st Annual Meeting) San· Francisco, California OctoberS December 898 March 4-5, 1995 Hartford, Connecticut 899 March 17-18, 1995 Orlando, Florida 900 March 24-25, 1995 Chicago, Illinois August 6-8, 1995 (97th Summer Meeting) Burlington, Vermont October -
Motives, Part 1
http://dx.doi.org/10.1090/pspum/055.1 Recent Titles in This Series 55 Uwe Jannsen, Steven Kleiman, and Jean-Pierre Serre, editors, Motives (University of Washington, Seattle, July /August 1991) 54 Robert Greene and S. T. Yan, editors, Differential geometry (University of California, Los Angeles, July 1990) 53 James A. Carlson, C. Herbert Clemens, and David R. Morrison, editors, Complex geometry and Lie theory (Sundance, Utah, May 1989) 52 Eric Bedford, John P. D'Angelo, Robert £. Greene, and Steven G. Krantz, editors, Several complex variables and complex geometry (University of California, Santa Cruz, July 1989) 51 William B. Arveson and Ronald G. Douglas, editors, Operator theory/operator algebras and applications (University of New Hampshire, July 1988) 50 James Glimm, John Impagliazzo, and Isadore Singer, editors, The legacy of John von Neumann (Hofstra University, Hempstead, New York, May/June 1988) 49 Robert C. Gunning and Leon Ehrenpreis, editors, Theta functions - Bowdoin 1987 (Bowdoin College, Brunswick, Maine, July 1987) 48 R. O. Wells, Jr., editor, The mathematical heritage of Hermann Weyl (Duke University, Durham, May 1987) 47 Paul Fong, editor, The Areata conference on representations of finite groups (Humboldt State University, Areata, California, July 1986) 46 Spencer J. Bloch, editor, Algebraic geometry - Bowdoin 1985 (Bowdoin College, Brunswick, Maine, July 1985) 45 Felix £. Browder, editor, Nonlinear functional analysis and its applications (University of California, Berkeley, July 1983) 44 William K. Allard and Frederick J. Almgren, Jr., editors, Geometric measure theory and the calculus of variations (Humboldt State University, Areata, California, July/August 1984) 43 Francois Treves, editor, Pseudodifferential operators and applications (University of Notre Dame, Notre Dame, Indiana, April 1984) 42 Anil Nerode and Richard A. -
View This Volume's Front and Back Matter
University LECTURE Series Volume 63 Noncommutative Motives Gonçalo Tabuada American Mathematical Society Noncommutative Motives http://dx.doi.org/10.1090/ulect/063 University LECTURE Series Volume 63 Noncommutative Motives Gonçalo Tabuada American Mathematical Society Providence, Rhode Island EDITORIAL COMMITTEE Jordan S. Ellenberg Robert Guralnik William P. Minicozzi II (Chair) Tatiana Toro 2010 Mathematics Subject Classification. Primary 14A22, 14C15, 18D20; Secondary 18E30, 18G55, 19D55. For additional information and updates on this book, visit www.ams.org/bookpages/ulect-63 Library of Congress Cataloging-in-Publication Data Tabuada, Gon¸calo, 1979– Noncommutative motives / Gon¸calo Tabuada. pages cm. – (University lecture series ; volume 63) Includes bibliographical references and index. ISBN 978-1-4704-2397-1 (alk. paper) 1. Motives (Mathematics) 2. Noncommutative algebras. 3. Algebraic varieties. I. Title. QA564.T33 2015 516.35–dc23 2015018204 Copying and reprinting. Individual readers of this publication, and nonprofit libraries acting for them, are permitted to make fair use of the material, such as to copy select pages for use in teaching or research. Permission is granted to quote brief passages from this publication in reviews, provided the customary acknowledgment of the source is given. Republication, systematic copying, or multiple reproduction of any material in this publication is permitted only under license from the American Mathematical Society. Permissions to reuse portions of AMS publication content are handled by Copyright Clearance Center’s RightsLink service. For more information, please visit: http://www.ams.org/rightslink. Send requests for translation rights and licensed reprints to [email protected]. Excluded from these provisions is material for which the author holds copyright. -
BIBLIOGRAPHY References
BIBLIOGRAPHY References [AB57] Maurice Auslander and David A. Buchsbaum, Homological dimension in local rings, Trans. Amer. Math. Soc. 85 (1957), 390–405. [Abb00] Ahmed Abbes, Réduction semi-stable des courbes d’après Artin, Deligne, Grothendieck, Mumford, Saito, Winters, ..., Courbes semi-stables et groupe fonda- mental en géométrie algébrique (Luminy, 1998), Progr. Math., vol. 187, Birkhäuser, Basel, 2000, pp. 59–110. [Abb10] , Éléments de géométrie rigide. Volume I, Progress in Mathematics, vol. 286, Birkhäuser/Springer Basel AG, Basel, 2010. [ABD+66] Michael Artin, Jean-Etienne Bertin, Michel Demazure, Alexander Grothendieck, Pierre Gabriel, Michel Raynaud, and Jean-Pierre Serre, Schémas en groupes, Sémi- naire de Géométrie Algébrique de l’Institut des Hautes Études Scientifiques, Institut des Hautes Études Scientifiques, Paris, 1963/1966. [ACGH85] Enrico Arbarello, Maurizio Cornalba, Philip Augustus Griffiths, and Joseph Daniel Harris, Geometry of algebraic curves: Volume I, Grundlehren der mathematischen Wissenschaften, no. 267, Springer-Verlag, 1985. [Ach17] Piotr Achinger, Wild ramification and K(π, 1) spaces, Invent. Math. 210 (2017), no. 2, 453–499. [ACV03] Dan Abramovich, Alessio Corti, and Angelo Vistoli, Twisted bundles and admissible covers, Communications in Algebra 31 (2003), no. 8, 3547–3618, Special issue in honor of Steven L. Kleiman. [AD83] Michael Artin and Jan Denef, Smoothing of a ring homomorphism along a section, Arithmetic and geometry, Vol. II, Progr. Math., vol. 36, Birkhäuser Boston, Mass., 1983, pp. 5–31. [AGV71] Michael Artin, Alexander Grothendieck, and Jean-Louis Verdier, Theorie de topos et cohomologie etale des schemas I, II, III, Lecture Notes in Mathematics, vol. 269, 270, 305, Springer, 1971. [AGV08] Dan Abramovich, Tom Graber, and Angelo Vistoli, Gromov-Witten theory of Deligne-Mumford stacks, American Journal of Mathematics 130 (2008), no.