Noncommutative Geometry and Number Theory Where Arithmetic meets Geo
In recent years, number theory and arithmetic geometry have been enriched by new techniques from noncommutative geometry, operator algebras, dynamical systems, and K-Theory. This volume collects and presents up-to-date research topics in arithmetic and no
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Noncommutative Geometry and Number Theory
Aspects of Mathematics Edited by Klas Diederich
Vol. E 6: G. Faltings/G. Wüstholz et al.: Rational Points* Vol. E 15: J .-P. Serre: Lectures on the Mordell-Weil Theorem Vol. E 16: K. Iwasaki/H. Kimura/S. Shimemura/M. Yoshida: From Gauss to Painlevé Vol. E 19: R. Racke: Lectures on Nonlinear Evolution Equations Vol. E 21: H. Fujimoto: Value Distribution Theory of the Gauss Map of Minimal Surfaces in Rm Vol. E22: D. V. Anosov/A. A. Bolibruch: The Riemann-Hilbert Problem Vol. E 27: D. N. Akhiezer: Lie Group Actions in Complex Analysis Vol. E28: R. Gérard/H. Tahara: Singular Nonlinear Partial Differential Equations Vol. E34: I. Lieb/J. Michel: The Cauchy-Riemann Complex Vol. E36: C. Hertling/M. Marcolli (Eds.): Frobenius Manifolds* Vol. E 37: C. Consani/M. Marcolli (Eds.): Noncommutative Geometry and Number Theory*
*A Publication of the Max-Planck-lnstitute for Mathematics, Bonn
Caterina Consani Matilde Marcolli (Eds.)
Noncommutative Geometry and Number Theory Where Arithmetic meets Geometry and Physics A Publication of the Max-Planck-Institute for Mathematics, Bonn
Bibliografische information published by Die Deutsche Bibliothek Die Deutsche Bibliothek lists this publication in the Deutschen Nationalbibliografie; detailed bibliographic data is available in the Internet at .
Prof. Dr. Caterina Consani Department of Mathematics The Johns Hopkins University 3400 North Charles Street Baltimore, MD 21218, USA [email protected] Prof. Dr. Matilde Marcolli Max-Planck-Institut für Mathematik Vivatsgasse 7 D-53111 Bonn [email protected] Prof. Dr. Klas Diederich (Series Editor) Fachbereich Mathematik Bergische Universität Wuppertal Gaußstraße 20 D-42119 Wuppertal [email protected] Mathematics Subject Classification Primary: 58B34, 11X Secondary: 11F23, 11S30, 11F37, 11F41, 11F70, 11F80, 11J71, 11B57, 11K36, 11F32, 11F75, 11G18, 14A22, 14F42, 14G05, 14G40, 14K10, 14G35, 18E30, 19D55, 20G05, 22E50, 32G05, 46L55, 58B34, 58E20, 70S15, 81T40. First edition, March 2006 All rights reserved © Friedr. Vieweg & Sohn Verlag | GWV Fachverlage GmbH, Wiesbaden 2006 Editorial Office: Ulrike Schmickler-Hirzebruch / Petra Rußkamp Vieweg is a company in the specialist publishing group Springer Science+Business Media. www.vieweg.de
No part of this publication may be reproduced, stored in a retrieval system or transmitted, mechanical, photocopying or otherwise without prior permission of the copyright holder.
Cover design: Ulrike Weigel, www.CorporateDesignGroup.de Printing and binding: MercedesDruck, Berlin Printed on acid-free paper Printed in Germany
ISBN 3-8348-0170-4
ISSN 0179-2156
Preface In recent years, number theory and arithmetic geometry have been enriched by new techniques from noncommutative geometry, operator algebras, dynamical systems, and K-Theory. Research across these fields has now reached an important turning point, as shows the increasing interest with which the mathematical community approaches these topics. This volume collects and presents up-to-date researc
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