Name: Weil's Conjecture for Function Fields: Volume i (Ams-199) (Annals of Mathematics Studies) (en Inglés)
SKU: 51501734
Price: 304.11 USD
Availability: InStock
Author: Dennis Gaitsgory; Jacob Lurie
ISBN: 9780691182131

portada Weil's Conjecture for Function Fields: Volume i (Ams-199) (Annals of Mathematics Studies) (en Inglés)

Weil's Conjecture for Function Fields: Volume i (Ams-199) (Annals of Mathematics Studies) (en Inglés)

Formato

Libro Físico

Editorial

Princeton University Press

Autor

Dennis Gaitsgory; Jacob Lurie

Año

2019

Idioma

Inglés

N° páginas

320

Encuadernación

Tapa Dura

ISBN13

9780691182131

N° edición

Categorías

Geometría algebraica

Weil's Conjecture for Function Fields: Volume i (Ams-199) (Annals of Mathematics Studies) (en Inglés)

Dennis Gaitsgory; Jacob Lurie (Autor) · Princeton University Press · Tapa Dura

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Reseña del libro "Weil's Conjecture for Function Fields: Volume i (Ams-199) (Annals of Mathematics Studies) (en Inglés)"

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.