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Weil's Conjecture for Function Fields: Volume I (AMS-199) (Annals of Mathematics Studies Book 360) 🔍
Gaitsgory, Dennis ;Lurie, Jacob Princeton University Press, Annals of Mathematics Studies; 199, 2019 dec 31
英语 [en] · PDF · 2.0MB · 2019 · 📘 非小说类图书 · 🚀/lgli/lgrs/nexusstc/upload/zlib · Save
描述
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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nexusstc/Weil's Conjecture for Function Fields: Volume I (AMS-199)/ebdaf165a074ac3a42b799c7a5302530.pdf
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lgli/10.1515_9780691184432.pdf
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zlib/no-category/Dennis Gaitsgory; Jacob Lurie/Weil's Conjecture for Function Fields: Volume I (AMS-199)_25975692.pdf
备选标题
Weil's Conjecture for Function Fields: Volume I (AMS-199) (Annals of Mathematics Studies, 199)
备选作者
Dennis Gaitsgory; Jacob Lurie
备用出版商
Princeton University, Department of Art & Archaeology
备用版本
Annals of mathematics studies, Princeton, New Jersey, 2019
备用版本
Annals of mathematics studies, no. 199, Princeton, 2019
备用版本
Princeton University Press, Princeton, 2019
备用版本
United States, United States of America
备用版本
Feb 19, 2019
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degruyter.com
元数据中的注释
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{"isbns":["0691182140","0691184437","9780691182148","9780691184432"],"last_page":320,"publisher":"Princeton University Press","series":"Annals of Mathematics Studies; 199"}
元数据中的注释
Source title: Weil's Conjecture for Function Fields: Volume I (AMS-199) (Annals of Mathematics Studies)
备用描述
"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{u2019}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{u2019}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{u2019}s conjecture. The proof of the product formula will appear in a sequel volume."--Publisher's description
备用描述
"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." -- Provided by publisher (for v.1)
备用描述
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.
备用描述
Contents
Chapter One. Introduction
Chapter Two. The Formalism of l-adic Sheaves
Chapter Three. E∞-Structures on l-Adic Cohomology
Chapter Four. Computing the Trace of Frobenius
Chapter Five The Trace Formula for Bun G (X)
Bibliography
开源日期
2023-08-25
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