Weil Conjectures, Perverse Sheaves and ¿-adic Fourier Transform

1. Auflage. Softcover version of original hardcover Auflage 2001
ISBN: 978-3-642-07472-1
Verlag: Springer

Buch, Englisch, Band 42, 375 Seiten, Previously published in hardcover, Format (B × H): 155 mm x 235 mm, Gewicht: 593 g

Reihe: Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics

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.

Zielgruppe

Research

Autoren/Hrsg.

Weissauer, Rainer

Kiehl, Reinhardt

Fachgebiete

• Mathematik | Informatik Mathematik Algebra Algebraische Strukturen, Gruppentheorie
• Mathematik | Informatik Mathematik Geometrie Algebraische Geometrie
• Mathematik | Informatik Mathematik Mathematische Analysis Harmonische Analysis, Fourier-Mathematik
• Mathematik | Informatik Mathematik Algebra Homologische Algebra

Inhaltsverzeichnis

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.