{"product_id":"weils-conjecture-for-function-fields-volume-i-annals-of-mathematics-studies","title":"Weils Conjecture for Function Fields: Volume I (Annals of Mathematics Studies)","description":"\u003cp\u003eA central concern of number theory is the study of localtoglobal 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 localtoglobal principle: Weils 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 Gbundles 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 Weils conjecture, based on the geometry of the moduli stack of Gbundles. Inspired by ideas from algebraic topology, it introduces a theory of factorization homology in the setting ladic sheaves. Using this theory, Dennis Gaitsgory and Jacob Lurie articulate a different localtoglobal principle: a product formula that expresses the cohomology of the moduli stack of Gbundles (a global object) as a tensor product of local factors.Using a version of the GrothendieckLefschetz trace formula, Gaitsgory and Lurie show that this product formula implies Weils conjecture. The proof of the product formula will appear in a sequel volume.\u003c\/p\u003e","brand":"Princeton University Press","offers":[{"title":"Gaitsgory, Dennis \/ paperback","offer_id":47846852559093,"sku":"DADAX0691182140","price":111.89,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0737\/5804\/8501\/files\/61UP73y6BPL.jpg?v=1773843737","url":"https:\/\/ergodebooks.com\/products\/weils-conjecture-for-function-fields-volume-i-annals-of-mathematics-studies","provider":"Ergodebooks","version":"1.0","type":"link"}