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| fixed length control field |
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| 008 - FIXED-LENGTH DATA ELEMENTS--GENERAL INFORMATION |
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| fixed length control field |
230418b xxu||||| |||| 00| 0 eng d |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER |
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| International Standard Book Number |
9780691182148 |
| 082 ## - DEWEY DECIMAL CLASSIFICATION NUMBER |
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| Classification number |
516.352 |
| Item number |
GAI |
| 100 ## - MAIN ENTRY--PERSONAL NAME |
|---|
| Personal name |
Gaitsgory, Dennis |
| 245 ## - TITLE STATEMENT |
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| Title |
Weil's Conjecture for Function Fields : Volume I |
| 260 ## - PUBLICATION, DISTRIBUTION, ETC. (IMPRINT) |
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| 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 |
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| Bibliography, etc |
Includes bibliographical references |
| 520 ## - SUMMARY, ETC. |
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| 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 |
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| Topical term or geographic name as entry element |
Weil conjectures |
|
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| Topical term or geographic name as entry element |
Geometry Algebraic |
|
|---|
| Topical term or geographic name as entry element |
Mathematics |
| 700 ## - ADDED ENTRY--PERSONAL NAME |
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| Personal name |
Lurie, Jacob |
| 942 ## - ADDED ENTRY ELEMENTS (KOHA) |
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| Source of classification or shelving scheme |
|
| Item type |
Books |