Weil's Conjecture for Function Fields: Volume I (AMS-199) (Annals of Mathematics Studies)
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Weil's Conjecture for Function Fields: Volume I (AMS-199) (Annals of Mathematics Studies)

Weil's Conjecture for Function Fields: Volume I (AMS-199) (Annals of Mathematics Studies)

By
Dennis Gaitsgory (Author) Jacob Lurie (Author)  

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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.
Dennis Gaitsgory is professor of mathematics at Harvard University. He is the coauthor of A Study in Derived Algebraic Geometry. Jacob Lurie is professor of mathematics at Harvard University. He is the author of Higher Topos Theory (Princeton).
  • Contributor: Dennis Gaitsgory
  • Imprint: Princeton University Press
  • ISBN13: 9780691182148
  • Number of Pages: 320
  • Packaged Dimensions: 155x235mm
  • Format: Paperback
  • Publisher: Princeton University Press
  • Release Date: 2019-03-08
  • Series: Annals of Mathematics Studies
  • Binding: Paperback / softback
  • Biography: Dennis Gaitsgory is professor of mathematics at Harvard University. He is the coauthor of A Study in Derived Algebraic Geometry. Jacob Lurie is professor of mathematics at Harvard University. He is the author of Higher Topos Theory (Princeton).

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