000			a
999			_c31937 _d31937
008			230418b xxu||||| |||| 00| 0 eng d
020			_a9780691182148
082			_a516.352 _bGAI
100			_aGaitsgory, Dennis
245			_aWeil's Conjecture for Function Fields : Volume I
260			_bPrinceton University Press, _a2019 _cPrinceton :
300			_aviii, 311 p. ; _bill., _c24 cm
365			_b80.00 _cUSD _d85.90
490			_vv.1
504			_aIncludes bibliographical references
520			_aA 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.
650			_aWeil conjectures
650			_aGeometry Algebraic
650			_aMathematics
700			_aLurie, Jacob
942			_2ddc _cBK