Eisensteinkohomologie und die Konstruktion gemischter Motive
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1562
Gunter Harder
Eisensteinkohomologie
und die Konstruktion gemischter Motive
Springer-Verlag Berlin Heidelberg New York London Paris Tokyo Hong Kong Barcelona Budapest
Author Gunter Harder Mathematisches Institut Universitat Bonn BeringstraBe 6 D-53115 Bonn, Germany
Mathematics Subject Classification (1991): 11F67, 11F75, 11F80, 11G18, 11G40 ISBN 3-540-57408-5 Springer-Verlag Berlin Heidelberg New York ISBN 0-387-57408-5 Springer-Verlag New York Berlin Heidelberg This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, re-use of illustrations, recitation, broadcasting, reproduction on microfilms or in any other way, and storage in data banks. Duplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law of September 9, 1965, in its current version, and permission for use must always be obtained from Springer-Verlag. Violations are liable for prosecution under the German Copyright Law. © Springer-Verlag Berlin Heidelberg 1993 Printed in Germany
2146/3140-543210 - Printed on acid-free paper
Introduction This volume grew out of a series of talks which I gave in the "Seminar iiber automorphe Formen " at the University of Bonn during the winter term 1988/89. A preliminary version of this manuscript was distributed in summer 1989 and a revised version circulated since summer 1991. The text is written in German because it is based on the talks in the above seminar. On request of the editors of the Lecture Notes I am writing an introduction in English which hopefully will be helpful for readers who are not familiar with German. In this introduction I will give a rather extended description of the contents of the individual Chapters. The idea is that a reader who gets stuck because of the language problem may get some help here in the introduction. In this introduction I will give no references to the literature but rather to the corresponding place in the volume. There one hopefully also finds the correct references. Another paper that gives some kind of introduction to this volume is my address at the ICM in Kyoto in 1990. Before I give the more detailed desription of the content of the book I give a very global overview. The goal of this book is to produce evidence that Shimura varieties provide a tool to construct certain objects (the mixed motives) which are predicted by the BeilinsonDeligne conjectures. These BeilinsonDeligne conjectures assert a connection between the behavior of the Lfunction of a motive at certain integer arguments and diophantine properties of this motive. They predict that the order of vanishing of the Lfunction at these specific arguments is equal the dimension of a certain space of extensions of the given motive by a Tate motive. These extensions become visible in the cohomology of suitable open algebraic varieties which have to be defined over certain number field. The problem is how to construct these varieties. T
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