Weil Conjectures, Perverse Sheaves and l’adic Fourier Transform

Abstract

Library of Congress Cataloging-in-Publication Data Kiehl, Reinhardt. Weil coniectures, perverse sheaves, and l-adic Fourier transform / Reinhardt Kiehl, Rainer Weissauer. p. cm.-(Ergebnisse der Mathematik und ihrer Grenzgebiete; 3. Folge, v. 42) Includes bibliographica! references and index.

L-Functions and Monodromy: Four Lectures on Weil II

“…As Kiehl and Weissauer point out in [KW,9.2 and 9.3], one can use this result, together with Deligne's monodromy analysis for individual curves over finite fields (i.e.``just'' 1.8.4]), to give an alternate derivation of the main theorem 3.3.1 of Weil II from the target theorem.…”

Geometric realizations of Lusztig's symmetries

“…By the properties of i χ n and i χ n (Theorem III.12.1(4,5) in [7]), we have the following commutative diagram…”

An introduction to perverse sheaves

“…See also [19,Chapter 8] and the nice introduction to Whitney stratifications in [15, Part I Chapter 1]. In general references for the theory of perverse sheaves include [1], [19], [22], and the encyclopedic [12].…”

“…Another reference for the ℓ-adic theory of perverse sheaves (including the decomposition theorem) is [22]. A proof of the decomposition theorem without the base change was given by M. Saito [28].…”