Weil's Conjecture for Function Fields: Volume I: 1 (Annals of Mathematics Studies, 199) - Tapa blanda

Libro 190 de 202: Annals of Mathematics Studies

Gaitsgory, Dennis; Lurie, Jacob

 
9780691182148: Weil's Conjecture for Function Fields: Volume I: 1 (Annals of Mathematics Studies, 199)
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ISBN 10: 0691182140 ISBN 13: 9780691182148
Editorial: Princeton University Press, 2019

Sinopsis

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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Acerca del autor

Dennis Gaitsgory is professor of mathematics at Harvard University. He is the coauthor of A Study in Derived Algebraic Geometry. Jacob Lurie is professor of mathematics at Harvard University. He is the author of Higher Topos Theory (Princeton).

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Editorial
Princeton University Press
Año de publicación
2019
Idioma
Inglés
ISBN 10 
0691182140
ISBN 13 
9780691182148
Encuadernación
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Número de páginas
320
Contacto del fabricante
no disponible
Persona responsable
no disponible

Otras ediciones populares con el mismo título

9780691182131: Weil's Conjecture for Function Fields: Volume I: 1 (Annals of Mathematics Studies, 199)

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ISBN 10:  0691182132 ISBN 13:  9780691182131
Editorial: Princeton University Press, 2019
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