Weil s Conjecture for Function Fields is popular PDF and ePub book, written by Dennis Gaitsgory in 2019-02-19, it is a fantastic choice for those who relish reading online the Mathematics genre. Let's immerse ourselves in this engaging Mathematics book by exploring the summary and details provided below. Remember, Weil s Conjecture for Function Fields can be Read Online from any device for your convenience.
Weil s Conjecture for Function Fields Book PDF Summary
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.
Detail Book of Weil s Conjecture for Function Fields PDF
- Author : Dennis Gaitsgory
- Release : 19 February 2019
- Publisher : Princeton University Press
- ISBN : 9780691182148
- Genre : Mathematics
- Total Page : 320 pages
- Language : English
- PDF File Size : 17,5 Mb
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