Weil's conjecture for function fields. Volume I /

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...

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Detalles Bibliográficos
Clasificación:Libro Electrónico
Autores principales: Gaitsgory, D. (Dennis) (Autor), Lurie, Jacob, 1977- (Autor)
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Princeton : Princeton University Press, 2019.
Colección:Annals of mathematics studies ; no. 199.
Temas:
Weil conjectures.
Conjectures de Weil.
MATHEMATICS > Geometry > General.
MATHEMATICS > Geometry > Algebraic.
Weil conjectures
Frobenius automorphism.
G-bundles.
Grothendieck-Lefschetz.
Weil's conjecture.
Weill's conjecture.
affine group.
algebraic geometry.
algebraic topology.
analogue.
cohomology.
continuous Künneth decomposition.
factorization homology.
function fields.
global "ient stacks.
infinity.
local-to-global principle.
moduli stack.
number theory.
rational functions.
sheaves.
trace formula.
triangulated category.
Acceso en línea:Texto completo
Descripción
Sumario: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.
Descripción Física:1 online resource
Bibliografía:Includes bibliographical references.
ISBN:9780691184432
0691184437

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