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Weil's Conjecture for Function Fields – Volume I (AMS-199) - Princeton Scholarship Online
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Weil's Conjecture for Function Fields: Volume I (AMS-199)

Dennis Gaitsgory and Jacob Lurie


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 ... More

Keywords: number theory, Weil's conjecture, G-bundles, algebraic topology, factorization homology, local-to-global principle, cohomology

Bibliographic Information

Print publication date: 2019 Print ISBN-13: 9780691182148
Published to Princeton Scholarship Online: September 2019 DOI:10.23943/princeton/9780691182148.001.0001


Affiliations are at time of print publication.

Dennis Gaitsgory, author
Harvard University

Jacob Lurie, author
Harvard University