Vollständige Systeme Modaler Und Intuitionistischer Logik (ergebnisse Der Mathematik Und Ihrer Grenzgebiete. 2. Folge) (german Edition)

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. 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. Front Matter....Pages I-VII Modalitätensysteme im Rahmen der klassischen Prädikatenlogik....Pages 1-11 Syntaktische Eigenschaften schnittfreier Modalitätensysteme....Pages 12-21 Beweis des Vollständigkeitssatzes für M ′ und S 4′....Pages 22-32 Einbettung der intuitionistischen Prädikatenlogik in S 4′....Pages 33-43 Semantik der intuitionistischen Prädikatenlogik nach Kripke ....Pages 44-59 Semantik der intuitionistischen Prädikatenlogik nach Beth ....Pages 60-70 Aussagenlogische Modalitätensysteme....Pages 71-84 Back Matter....Pages 85-88 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 -- App. A. Q-sheaves -- App. B. Bertini Theorem For Etale Sheaves -- App. C. Kummer Extensions -- App. D. Finiteness Theorems. Reinhardt Kiehl, Rainer Weissauer. Includes Bibliographical References And Index.