🎉   Please check out our new website over at books-etc.com.

Seller
Your price
£43.23
RRP: £70.00
Save £26.77 (38%)
Dispatched within 2-3 working days.

Weil's Conjecture for Function Fields

Volume I (AMS-199). Annals of Mathematics Studies

Format: Paperback / softback
Publisher: Princeton University Press, New Jersey, United States
Published: 19th Feb 2019
Dimensions: w 151mm h 229mm d 20mm
Weight: 540g
ISBN-10: 0691182140
ISBN-13: 9780691182148
Barcode No: 9780691182148
Trade or Institutional customer? Contact us about large order quotes.
Synopsis
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.

New & Used

Seller Information Condition Price
-New£43.23
+ FREE UK P & P

What Reviewers Are Saying

Submit your review
Newspapers & Magazines
"The book is written in a clear and vivid style, pays attention to foundations and details, and yet elucidates motivations and ideas. It should be highly useful for researchers working with stacks and higher category theory."---Stefan Schroeer, Zentralblatt MATH