Reinhardt Kiehl Livres

Focusing on l-adic cohomology, this book presents an accessible introduction to etale and l-adic cohomology theory, including monodromy theory related to Lefschetz pencils. Originally prepared as notes for a conference on Deligne's proof of the Weil conjectures, the authors expanded these notes to provide a self-contained exploration of the topic. It incorporates historical insights from Professor J. A. Dieudonne and has been translated into English, thanks to the efforts of Professor W. Waterhouse and his wife.

Focusing on the generalization of the Weil conjectures, the authors present a simplified approach based on the methodologies of Laumon and Brylinski, enhancing Deligne's original theories. They delve into the sheaf theoretic framework of perverse sheaves, clarifying Deligne's concepts of global weights and purity of complexes. The book includes a comprehensive treatment of middle perverse sheaves and introduces the l-adic Fourier transform for straightforward proofs. Additionally, it features three chapters dedicated to significant applications of these theories.

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.