Eisensteinkohomologie und die Konstruktion gemischter Motive (Lecture Notes in Mathematics, 1562) (German Edition)

Harder, Günter

ISBN 10: 3540574085 / ISBN 13: 9783540574088

Editore: Springer, 1993

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Codice articolo 4CNO3J0051G1

Dati bibliografici

• Titolo: Eisensteinkohomologie und die Konstruktion gemischter Motive (Lecture Notes in Mathematics, 1562) (German Edition)
• Editore: Springer
• Data di pubblicazione: 1993
• Lingua: Tedesco
• ISBN 10: 3540574085
• ISBN 13: 9783540574088
• Rilegatura: Brossura
• Condizione: LikeNew

Descrizione articolo

Riassunto

The aim of this book is to show that Shimura varietiesprovide a tool to construct certain interesting objects inarithmetic algebraic geometry. These objects are theso-called mixed motives: these are of great arithmeticinterest. They can be viewed as quasiprojective algebraicvarieties over Q which have some controlled ramification andwhere we know what we have to add at infinity to compactifythem.The existence of certain of these mixed motives is relatedto zeroes of L-functions attached to certain pure motives.This is the content of the Beilinson-Deligne conjectureswhich are explained in some detail in the first chapter ofthe book.The rest of the book is devoted to the description of thegeneral principles of construction (Chapter II) and thediscussion of several examples in Chapter II-IV. In anappendix we explain how the (topological) trace formula canbe used to get some understanding of the problems discussedin the book.Only some of this material is really proved: the book alsocontains speculative considerations, which give some hintsas to how the problems could be tackled. Hence the bookshould be viewed as the outline of a programme and it offerssome interesting problems which are of importance and can bepursued by the reader.In the widest sense the subject of the paper is numbertheory and belongs to what is called arithmetic algebraicgeometry. Thus the reader should be familiar with somealgebraic geometry, number theory, the theory of Liegroupsand their arithmetic subgroups. Some problems mentionedrequire only part of this background knowledge.

Contenuti

Die Beilinson-Deligne-Vermutungen.- Die Kohomologie von Shimura-Varietäten.- Die Beispiele.- Andersons gemischte Motive.