Author	Kiehl, Reinhardt. author
Title	Weil Conjectures, Perverse Sheaves and l'adic Fourier Transform [electronic resource] / by Reinhardt Kiehl, Rainer Weissauer
Imprint	Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 2001
Connect to	http://dx.doi.org/10.1007/978-3-662-04576-3
Descript	XII, 375 p. online resource

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

I. The General Weil Conjectures (Deligne's Theory of Weights) -- II. The Formalism of Derived Categories -- III. Perverse Sheaves -- IV. Lefschetz Theory and the BrylinskiโRadon Transform -- V. Trigonometric Sums -- VI. The Springer Representations -- B. Bertini Theorem for Etale Sheaves -- C. Kummer Extensions -- D. Finiteness Theorems

1. Mathematics
2. Algebraic geometry
3. Group theory
4. K-theory
5. Mathematics
6. Algebraic Geometry
7. Group Theory and Generalizations
8. K-Theory