Weil's Conjecture for Function Fields - Volume I (AMS-199) (Paperback)

A central concern of number theory is the study of local-to-global principles, which describe the behavior of a global field K in terms of the behavior of various completions of K. This book looks at a specific example of a local-to-global principle: Weil's conjecture on the Tamagawa number of a semisimple algebraic group G over K. In the case where K is the function field of an algebraic curve X, this conjecture counts the number of G-bundles on X (global information) in terms of the reduction of G at the points of X (local information). The goal of this book is to give a conceptual proof of Weil's conjecture, based on the geometry of the moduli stack of G-bundles. Inspired by ideas from algebraic topology, it introduces a theory of factorization homology in the setting -adic sheaves. Using this theory, Dennis Gaitsgory and Jacob Lurie articulate a different local-to-global principle: a product formula that expresses the cohomology of the moduli stack of G-bundles (a global object) as a tensor product of local factors. Using a version of the Grothendieck-Lefschetz trace formula, Gaitsgory and Lurie show that this product formula implies Weil's conjecture. The proof of the product formula will appear in a sequel volume.

General

Imprint:	Princeton University Press
Country of origin:	United States
Series:	Annals of Mathematics Studies
Release date:	February 2019
First published:	2019
Authors:	Dennis Gaitsgory • Jacob Lurie
Dimensions:	235 x 155 x 26mm (L x W x T)
Format:	Paperback - Trade
Pages:	320
ISBN-13:	978-0-691-18214-8
Categories:	Books > Science & Mathematics > Mathematics > Geometry > Algebraic geometry Books > Science & Mathematics > Mathematics > Number theory > General Promotions
LSN:	0-691-18214-0
Barcode:	9780691182148

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