WEIL CONJECTURES PERVERSE SHEAVES AND L'ADIC FOURIER TRANSFORM

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Ouvrage 9783540414575 : WEIL CONJECTURES PERVERSE SHEAVES AND L'ADIC FOURIER TRANSFORM

Kiehl, R., University of Mannheim, Germany; Weissauer, R., University of Mannheim, Germany
Weil Conjectures, Perverse Sheaves and l'adic Fourier Transform
2001. XII, 375 pp. Hardcover
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.
Keywords: Etale cohomology, generalized Weil conjecture, Deligne ' s theory of weights and of purity, middle perverse sheaves, Deligne ' s Fourier transform, Hard Lefschetz Theorem, estimates of exponential sums, Springer representations Weyl groups .
Series: Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics. VOL. 42


Auteur : KIEHL
Editeur : SPRINGER VERLAG
Nombre de pages : 375
Date de publication : 10 2001

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