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Mathematics - Algebra | Weil Conjectures, Perverse Sheaves and l’adic Fourier Transform

Weil Conjectures, Perverse Sheaves and l’adic Fourier Transform

Kiehl, Reinhardt, Weissauer, Rainer

2001, XII, 375 p.

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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.

Content Level » Research

Keywords » Deligne's Fourier transform - Deline's theory of weights and of purity - Etale cohomology - Hard Lefschetz Theorem - Springer representations Weyl groups - estimates of exponential sums - generalized Weil conjecture - middle perverse sheaves

Related subjects » Algebra

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