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Titlebook: Etale Cohomology and the Weil Conjecture; Eberhard Freitag,Reinhardt Kiehl Book 1988 Springer-Verlag Berlin Heidelberg 1988 Abelian variet

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书目名称Etale Cohomology and the Weil Conjecture
编辑Eberhard Freitag,Reinhardt Kiehl
视频video
丛书名称Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathemati
图书封面Titlebook: Etale Cohomology and the Weil Conjecture;  Eberhard Freitag,Reinhardt Kiehl Book 1988 Springer-Verlag Berlin Heidelberg 1988 Abelian variet
描述Some years ago a conference on l-adic cohomology in Oberwolfach was held with the aim of reaching an understanding of Deligne‘s proof of the Weil conjec­ tures. For the convenience of the speakers the present authors - who were also the organisers of that meeting - prepared short notes containing the central definitions and ideas of the proofs. The unexpected interest for these notes and the various suggestions to publish them encouraged us to work somewhat more on them and fill out the gaps. Our aim was to develop the theory in as self­ contained and as short a manner as possible. We intended especially to provide a complete introduction to etale and l-adic cohomology theory including the monodromy theory of Lefschetz pencils. Of course, all the central ideas are due to the people who created the theory, especially Grothendieck and Deligne. The main references are the SGA-notes [64-69]. With the kind permission of Professor J. A. Dieudonne we have included in the book that finally resulted his excellent notes on the history of the Weil conjectures, as a second introduction. Our original notes were written in German. However, we finally followed the recommendation made variously to
出版日期Book 1988
关键词Abelian varieties; Abelian variety; algebraic geometry; cohomology; collaboration; development; diophantin
版次1
doihttps://doi.org/10.1007/978-3-662-02541-3
isbn_softcover978-3-662-02543-7
isbn_ebook978-3-662-02541-3Series ISSN 0071-1136 Series E-ISSN 2197-5655
issn_series 0071-1136
copyrightSpringer-Verlag Berlin Heidelberg 1988
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Schlussbetrachtuog und Ausblick,The aim of this book is to develop Grothendieck’s etale cohomology theory of algebraic varieties as far as necessary and then to present Deligne’s proof of the Weil conjecture using this cohomology.
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Martin Reckenfelderbäumer,Christian ArnoldThe goal of this chapter is to prove the rationality of the Weil ζ-function of an algebraic variety over a finite field, or more generally of the .-series for constructible sheaves (Theorem 4.4). Following Grothendieck, we will derive the rationality from a fixed point formula of Lefschetz type for the Frobenius morphism (Proposition 4.2).
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The Essentials of Etale Cohomology Theory,We start this chapter with an example, due to J-P. Serre, that illuminates some of the difficulties in constructing a Weil cohomology.
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,Rationality of Weil ζ-Functions,The goal of this chapter is to prove the rationality of the Weil ζ-function of an algebraic variety over a finite field, or more generally of the .-series for constructible sheaves (Theorem 4.4). Following Grothendieck, we will derive the rationality from a fixed point formula of Lefschetz type for the Frobenius morphism (Proposition 4.2).
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