Weil's Conjecture for Function Fields : : Volume I (AMS-199) / / Jacob Lurie, Dennis Gaitsgory.

• Superior document: Title is part of eBook package: De Gruyter EBOOK PACKAGE COMPLETE 2019 English
• VerfasserIn: Gaitsgory, Dennis,; Lurie, Jacob,
• Place / Publishing House: Princeton, NJ : : Princeton University Press, , [2019]; ©2019
• Year of Publication: 2019
• Language: English
• Series: Annals of Mathematics Studies ; 199
• Physical Description: 1 online resource (320 p.)
• Other title: Frontmatter --; Contents --; Chapter One. Introduction --; Chapter Two. The Formalism of ℓ-adic Sheaves --; Chapter Three. E∞-Structures on ℓ-Adic Cohomology --; Chapter Four. Computing the Trace of Frobenius --; Chapter Five The Trace Formula for BunG(X) --; Bibliography
• Format: Mode of access: Internet via World Wide Web.
• ISBN: 9780691184432; 9783110610765; 9783110664232; 9783110610406; 9783110606362; 9783110494914; 9783110663365
• DOI: 10.1515/9780691184432?locatt=mode:legacy
• Access: restricted access
• Hierarchical level: Monograph
• Statement of Responsibility: Jacob Lurie, Dennis Gaitsgory.

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.