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Author : Gérard Laumon
Release : 1996
Genre :
Kind : eBook
Book Rating : /5 ( reviews)
Book Synopsis Cohomology of Drinfeld Modular Varieties by : Gérard Laumon
Download or read book Cohomology of Drinfeld Modular Varieties written by Gérard Laumon. This book was released on 1996. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Gérard Laumon
Release : 1996
Genre : Mathematics
Kind : eBook
Book Rating : 609/5 ( reviews)
Book Synopsis Cohomology of Drinfeld Modular Varieties, Part 1, Geometry, Counting of Points and Local Harmonic Analysis by : Gérard Laumon
Download or read book Cohomology of Drinfeld Modular Varieties, Part 1, Geometry, Counting of Points and Local Harmonic Analysis written by Gérard Laumon. This book was released on 1996. Available in PDF, EPUB and Kindle. Book excerpt: Originally published in 1995, Cohomology of Drinfeld Modular Varieties aimed to provide an introduction, in two volumes, both to this subject and to the Langlands correspondence for function fields. These varieties are the analogues for function fields of the Shimura varieties over number fields. The Langlands correspondence is a conjectured link between automorphic forms and Galois representations over a global field. By analogy with the number-theoretic case, one expects to establish the conjecture for function fields by studying the cohomology of Drinfeld modular varieties, which has been done by Drinfeld himself for the rank two case. The present volume is devoted to the geometry of these varieties, and to the local harmonic analysis needed to compute their cohomology. Though the author considers only the simpler case of function rather than number fields, many important features of the number field case can be illustrated.
Author : Gérard Laumon
Release : 2010-12-09
Genre : Mathematics
Kind : eBook
Book Rating : 745/5 ( reviews)
Book Synopsis Cohomology of Drinfeld Modular Varieties, Part 1, Geometry, Counting of Points and Local Harmonic Analysis by : Gérard Laumon
Download or read book Cohomology of Drinfeld Modular Varieties, Part 1, Geometry, Counting of Points and Local Harmonic Analysis written by Gérard Laumon. This book was released on 2010-12-09. Available in PDF, EPUB and Kindle. Book excerpt: Cohomology of Drinfeld Modular Varieties aims to provide an introduction to both the subject of the title and the Langlands correspondence for function fields. These varieties are the analogs for function fields of Shimura varieties over number fields. This present volume is devoted to the geometry of these varieties and to the local harmonic analysis needed to compute their cohomology. To keep the presentation as accessible as possible, the author considers the simpler case of function rather than number fields; nevertheless, many important features can still be illustrated. It will be welcomed by workers in number theory and representation theory.
Author : Gérard Laumon
Release : 2010-12-09
Genre : Mathematics
Kind : eBook
Book Rating : 745/5 ( reviews)
Book Synopsis Cohomology of Drinfeld Modular Varieties, Part 1, Geometry, Counting of Points and Local Harmonic Analysis by : Gérard Laumon
Download or read book Cohomology of Drinfeld Modular Varieties, Part 1, Geometry, Counting of Points and Local Harmonic Analysis written by Gérard Laumon. This book was released on 2010-12-09. Available in PDF, EPUB and Kindle. Book excerpt: Cohomology of Drinfeld Modular Varieties aims to provide an introduction to both the subject of the title and the Langlands correspondence for function fields. These varieties are the analogs for function fields of Shimura varieties over number fields. This present volume is devoted to the geometry of these varieties and to the local harmonic analysis needed to compute their cohomology. To keep the presentation as accessible as possible, the author considers the simpler case of function rather than number fields; nevertheless, many important features can still be illustrated. It will be welcomed by workers in number theory and representation theory.
Author : Reinhardt Kiehl
Release : 2013-03-14
Genre : Mathematics
Kind : eBook
Book Rating : 761/5 ( reviews)
Book Synopsis Weil Conjectures, Perverse Sheaves and l-adic Fourier Transform by : Reinhardt Kiehl
Download or read book Weil Conjectures, Perverse Sheaves and l-adic Fourier Transform written by Reinhardt Kiehl. This book was released on 2013-03-14. Available in PDF, EPUB and Kindle. Book excerpt: 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.
