Weil`s Conjecture for Function Fields – Volume I (AMS–199) (Annals of Mathematics Studies, 199) - Image 1

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Princeton University Press Weil`s Conjecture for Function Fields – Volume I (AMS–199) (Annals of Mathematics Studies, 199)

Name: Weil`s Conjecture for Function Fields - Volume I (AMS-199) (Annals of Mathematics Studies, 199)
Brand: Princeton University Press
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Higher Education

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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 ℓ-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.

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Brand: Princeton University Press
Format: hardcover
ASIN: 0691182132
Category: Books > Subjects > Science, Nature & Maths > Mathematics > Education > Higher Education
Domain: Amazon UK
Release Date: 08 March 2019
Listed Since: 26 April 2018

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Princeton University Press Weil`s Conjecture for Function Fields – Volume I (AMS–199) (Annals of Mathematics Studies, 199)

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