000			02838nam a22003257a 4500
003			OSt
005			20240511150941.0
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020			_a9783540574088
040			_aNISER LIBRARY _beng _cNISER LIBRARY
082			_a512.7 _bHAR-E
100			_aHarder, Gunter
245			_aEisensteinkohomologie und die konstruktion gemischter motive
260			_aNew York : _bSpringer-Verlag, _c1993.
300			_axx, 184p. ; _c24 cm.
490			_aLecture notes in mathematics ; _v1562 _x0075-8434
500			_aGerman with English introduction and appendix.
504			_aIncludes bibliographical references (p. [174]-178) and index.
520			_aThe 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 Chapter II-IV. In an appendix we explain 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 Liegroups and their arithmetic subgroups. Some problems mentioned require only part of this background knowledge.
650			_aShimura varieties.
650			_aAutomorphic forms.
650			_aL-functions.
650			_aShimura-Varietäten
650			_aZahlentheorie
650			_aAlgebraische Varietät
650			_aKohomologie
856			_uhttps://link.springer.com/book/10.1007/BFb0090305#toc _3Table of contents
856			_uhttps://www.goodreads.com/book/show/4261558-eisensteinkohomologie-und-die-konstruktion-gemischter-motive-lecture-no?from_search=true&from_srp=true&qid=f7plDe3H7W&rank=2#CommunityReviews _3Reviews
942			_2udc _cBK
999			_c34992 _d34992