Weil's conjecture for function fields:
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 sem...
Gespeichert in:
| Beteiligte Personen: | , |
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| Format: | Elektronisch E-Book |
| Sprache: | Englisch |
| Veröffentlicht: |
Princeton ; NJ
Princeton University Press
[2019]
|
| Schriftenreihe: | Annals of mathematics studies
Number 199 |
| Schlagwörter: | |
| Links: | https://doi.org/10.1515/9780691184432?locatt=mode:legacy https://doi.org/10.1515/9780691184432?locatt=mode:legacy https://doi.org/10.1515/9780691184432?locatt=mode:legacy https://doi.org/10.1515/9780691184432?locatt=mode:legacy https://doi.org/10.1515/9780691184432?locatt=mode:legacy https://doi.org/10.1515/9780691184432?locatt=mode:legacy https://www.degruyter.com/view/product/513016 https://doi.org/10.1515/9780691184432?locatt=mode:legacy https://doi.org/10.1515/9780691184432 |
| Zusammenfassung: | 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 |
| Umfang: | 1 Online-Ressource (v, 309 Seiten) |
| ISBN: | 9780691184432 |
| DOI: | 10.1515/9780691184432 |
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| 520 | |a 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 | ||
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| indexdate | 2025-02-18T17:10:37Z |
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| spelling | Gaitsgory, Dennis (DE-588)1182044891 aut Weil's conjecture for function fields Jacob Lurie ; Dennis Gaitsgory Princeton ; NJ Princeton University Press [2019] © 2019 1 Online-Ressource (v, 309 Seiten) txt rdacontent c rdamedia cr rdacarrier Annals of mathematics studies Number 199 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 In English MATHEMATICS / Geometry / Algebraic bisacsh Weil conjectures Algebraische Funktion (DE-588)4141836-0 gnd rswk-swf Zetafunktion (DE-588)4190764-4 gnd rswk-swf Algebraische Geometrie (DE-588)4001161-6 gnd rswk-swf Algebraische Geometrie (DE-588)4001161-6 s Zetafunktion (DE-588)4190764-4 s Algebraische Funktion (DE-588)4141836-0 s DE-604 Lurie, Jacob 1977- (DE-588)139905529 aut Annals of mathematics studies Number 199 (DE-604)BV040389493 199 https://doi.org/10.1515/9780691184432 Verlag URL des Erstveröffentlichers Volltext |
| spellingShingle | Gaitsgory, Dennis Lurie, Jacob 1977- Weil's conjecture for function fields Annals of mathematics studies MATHEMATICS / Geometry / Algebraic bisacsh Weil conjectures Algebraische Funktion (DE-588)4141836-0 gnd Zetafunktion (DE-588)4190764-4 gnd Algebraische Geometrie (DE-588)4001161-6 gnd |
| subject_GND | (DE-588)4141836-0 (DE-588)4190764-4 (DE-588)4001161-6 |
| title | Weil's conjecture for function fields |
| title_auth | Weil's conjecture for function fields |
| title_exact_search | Weil's conjecture for function fields |
| title_full | Weil's conjecture for function fields Jacob Lurie ; Dennis Gaitsgory |
| title_fullStr | Weil's conjecture for function fields Jacob Lurie ; Dennis Gaitsgory |
| title_full_unstemmed | Weil's conjecture for function fields Jacob Lurie ; Dennis Gaitsgory |
| title_short | Weil's conjecture for function fields |
| title_sort | weil s conjecture for function fields |
| topic | MATHEMATICS / Geometry / Algebraic bisacsh Weil conjectures Algebraische Funktion (DE-588)4141836-0 gnd Zetafunktion (DE-588)4190764-4 gnd Algebraische Geometrie (DE-588)4001161-6 gnd |
| topic_facet | MATHEMATICS / Geometry / Algebraic Weil conjectures Algebraische Funktion Zetafunktion Algebraische Geometrie |
| url | https://doi.org/10.1515/9780691184432 |
| volume_link | (DE-604)BV040389493 |
| work_keys_str_mv | AT gaitsgorydennis weilsconjectureforfunctionfields AT luriejacob weilsconjectureforfunctionfields |