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 ...
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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 -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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Add this copy of Weil's Conjecture for Function Fields: Volume I (Ams to cart. $65.34, good condition, Sold by Bonita rated 4.0 out of 5 stars, ships from Newport Coast, CA, UNITED STATES, published 2019 by Princeton University Press.
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Add this copy of Weil's Conjecture for Function Fields: Volume I to cart. $78.80, new condition, Sold by GreatBookPrices rated 4.0 out of 5 stars, ships from Columbia, MD, UNITED STATES, published 2019 by Princeton University Press.
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New. Trade paperback (US). Glued binding. 320 p. Annals of Mathematics Studies, 199. In Stock. 100% Money Back Guarantee. Brand New, Perfect Condition, allow 4-14 business days for standard shipping. To Alaska, Hawaii, U.S. protectorate, P.O. box, and APO/FPO addresses allow 4-28 business days for Standard shipping. No expedited shipping. All orders placed with expedited shipping will be cancelled. Over 3, 000, 000 happy customers.
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