| 000 -LEADER | |
|---|---|
| fixed length control field | a |
| 008 - FIXED-LENGTH DATA ELEMENTS--GENERAL INFORMATION | |
| fixed length control field | 230418b xxu||||| |||| 00| 0 eng d |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER | |
| International Standard Book Number | 9780691182148 |
| 082 ## - DEWEY DECIMAL CLASSIFICATION NUMBER | |
| Classification number | 516.352 |
| Item number | GAI |
| 100 ## - MAIN ENTRY--PERSONAL NAME | |
| Personal name | Gaitsgory, Dennis |
| 245 ## - TITLE STATEMENT | |
| Title | Weil's Conjecture for Function Fields : Volume I |
| 260 ## - PUBLICATION, DISTRIBUTION, ETC. (IMPRINT) | |
| Name of publisher, distributor, etc | Princeton University Press, |
| Place of publication, distribution, etc | 2019 |
| Date of publication, distribution, etc | Princeton : |
| 300 ## - PHYSICAL DESCRIPTION | |
| Extent | viii, 311 p. ; |
| Other physical details | ill., |
| Dimensions | 24 cm |
| 365 ## - TRADE PRICE | |
| Price amount | 80.00 |
| Price type code | USD |
| Unit of pricing | 85.90 |
| 490 ## - SERIES STATEMENT | |
| Volume number/sequential designation | v.1 |
| 504 ## - BIBLIOGRAPHY, ETC. NOTE | |
| Bibliography, etc | Includes bibliographical references |
| 520 ## - SUMMARY, ETC. | |
| Summary, etc | 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. |
| 650 ## - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name as entry element | Geometry Algebraic |
| Topical term or geographic name as entry element | Geometry |
| Topical term or geographic name as entry element | Algebraic mathematics |
| Topical term or geographic name as entry element | Number theory |
| Topical term or geographic name as entry element | Bun G |
| Topical term or geographic name as entry element | Cartesian fibration |
| Topical term or geographic name as entry element | Isomorphism |
| Topical term or geographic name as entry element | Quasi-projective K-scheme |
| Topical term or geographic name as entry element | Symmetric monoidal |
| Topical term or geographic name as entry element | Tensor product |
| 700 ## - ADDED ENTRY--PERSONAL NAME | |
| Personal name | Lurie, Jacob |
| 942 ## - ADDED ENTRY ELEMENTS (KOHA) | |
| Source of classification or shelving scheme | |
| Item type | Books |
No items available.