Dennis Gaitsgory Jacob Lurie - Weil's Conjecture for Function Fields

Dennis Gaitsgory Jacob Lurie - Weil's Conjecture for Function Fields

109,99 €

A central concern of number theory is the study of local-to-global principles, which describe the behavior of a global fieldKin terms of the behavior of various completions ofKThis book looks at a specific example of a local-to-global principle: Weil’s conjecture on the Tamagawa number of a semisimple algebraic group .GoverKIn...

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Produktbeschreibung

A central concern of number theory is the study of local-to-global principles, which describe the behavior of a global fieldKin terms of the behavior of various completions ofKThis book looks at a specific example of a local-to-global principle: Weil’s conjecture on the Tamagawa number of a semisimple algebraic group .GoverKIn the case where .Kis the function field of an algebraic curveX, this conjecture counts the number ofG-bundles onX(global information) in terms of the reduction ofGat the points ofX(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.
Marke Princeton University Press
EAN 9780691182148
ISBN 978-0-691-18214-8
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