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＜電子ブック＞
Weil Conjectures, Perverse Sheaves and ℓ-adic Fourier Transform / by Reinhardt Kiehl, Rainer Weissauer
(Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics. ISSN:21975655 ; 42)

版	1st ed. 2001.
出版者	(Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer)
出版年	2001
本文言語	英語
大きさ	XII, 375 p : online resource
著者標目	*Kiehl, Reinhardt author Weissauer, Rainer author SpringerLink (Online service)
件　名	LCSH:Algebraic geometry LCSH:Group theory LCSH:K-theory FREE:Algebraic Geometry FREE:Group Theory and Generalizations FREE:K-Theory
一般注記	I. The General Weil Conjectures (Deligne’s Theory of Weights) -- II. The Formalism of Derived Categories -- III. Perverse Sheaves -- IV. Lefschetz Theory and the Brylinski—Radon Transform -- V. Trigonometric Sums -- VI. The Springer Representations -- B. Bertini Theorem for Etale Sheaves -- C. Kummer Extensions -- D. Finiteness Theorems In this book the authors describe the important generalization of the original Weil conjectures, as given by P. Deligne in his fundamental paper "La conjecture de Weil II". The authors follow the important and beautiful methods of Laumon and Brylinski which lead to a simplification of Deligne's theory. Deligne's work is closely related to the sheaf theoretic theory of perverse sheaves. In this framework Deligne's results on global weights and his notion of purity of complexes obtain a satisfactory and final form. Therefore the authors include the complete theory of middle perverse sheaves. In this part, the l-adic Fourier transform is introduced as a technique providing natural and simple proofs. To round things off, there are three chapters with significant applications of these theories HTTP:URL=https://doi.org/10.1007/978-3-662-04576-3

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