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OverviewThe aim of this book is to show that Shimura varieties provide a tool to construct certain interesting objects in arithmetic algebraic geometry. These objects are the so-called mixed motives: these are of great arithmetic interest. They can be viewed as quasiprojective algebraic varieties over Q which have some controlled ramification and where we know what we have to add at infinity to compactify them. The existence of certain of these mixed motives is related to zeroes of L-functions attached to certain pure motives. This is the content of the Beilinson-Deligne conjectures which are explained in some detail in the first chapter of the book. The rest of the book is devoted to the description of the general principles of construction (Chapter II) and the discussion of several examples in Chapters II-IV. An appendix explains how the (topological) trace formula can be used to get some understanding of the problems discussed in the book. Only some of this material is really proved: the book also contains speculative considerations, which give some hints as to how the problems could be tackled. Hence the book should be viewed as the outline of a programme and it offers some interesting problems which are of importance and can be pursued by the reader. In the widest sense the subject of the paper is number theory and belongs to what is called arithmetic algebraic geometry. Thus the reader should be familiar with some algebraic geometry, number theory, the theory of Lie groups and their arithmetic subgroups. Some problems mentioned require only part of this background knowledge. Full Product DetailsAuthor: Günter HarderPublisher: Springer-Verlag Berlin and Heidelberg GmbH & Co. KG Imprint: Springer-Verlag Berlin and Heidelberg GmbH & Co. K Edition: 1993 ed. Volume: 1562 Dimensions: Width: 15.50cm , Height: 1.10cm , Length: 23.50cm Weight: 0.670kg ISBN: 9783540574088ISBN 10: 3540574085 Pages: 184 Publication Date: 29 November 1993 Audience: College/higher education , Professional and scholarly , Postgraduate, Research & Scholarly , Professional & Vocational Format: Paperback Publisher's Status: Active Availability: In Print  This item will be ordered in for you from one of our suppliers. Upon receipt, we will promptly dispatch it out to you. For in store availability, please contact us. Language: German, English Table of ContentsDie Beilinson-Deligne-Vermutungen.- Die Kohomologie von Shimura-Varietäten.- Die Beispiele.- Andersons gemischte Motive.ReviewsAuthor InformationTab Content 6Author Website:Countries AvailableAll regions |
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