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Weil's conjecture for function fields. Volume I /
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...
| Clasificación: | Libro Electrónico |
|---|---|
| Autores principales: | , |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Princeton :
Princeton University Press,
2019.
|
| Colección: | Annals of mathematics studies ;
no. 199. |
| Temas: | |
| Acceso en línea: | Texto completo |
MARC
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| 100 | 1 | |a Gaitsgory, D. |q (Dennis), |e author. | |
| 245 | 1 | 0 | |a Weil's conjecture for function fields. |n Volume I / |c Dennis Gaitsgory, Jacob Lurie. |
| 264 | 1 | |a Princeton : |b Princeton University Press, |c 2019. | |
| 300 | |a 1 online resource | ||
| 336 | |a text |b txt |2 rdacontent | ||
| 337 | |a computer |b c |2 rdamedia | ||
| 338 | |a online resource |b cr |2 rdacarrier | ||
| 490 | 1 | |a Annals of mathematics studies ; |v number 199 | |
| 588 | |a Online resource; title from PDF title page (EBSCO, viewed December 21, 2018). | ||
| 504 | |a Includes bibliographical references. | ||
| 505 | 0 | |a The formalism of l-adic sheaves -- E∞-structures on l-adic cohomology -- Computing the trace of Frobenius -- The trace formula for BunG(X). | |
| 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. | ||
| 590 | |a JSTOR |b Books at JSTOR Demand Driven Acquisitions (DDA) | ||
| 590 | |a JSTOR |b Books at JSTOR Evidence Based Acquisitions | ||
| 590 | |a JSTOR |b Books at JSTOR All Purchased | ||
| 650 | 0 | |a Weil conjectures. | |
| 650 | 6 | |a Conjectures de Weil. | |
| 650 | 7 | |a MATHEMATICS |x Geometry |x General. |2 bisacsh | |
| 650 | 7 | |a MATHEMATICS |x Geometry |x Algebraic. |2 bisacsh | |
| 650 | 7 | |a Weil conjectures |2 fast | |
| 653 | |a Frobenius automorphism. | ||
| 653 | |a G-bundles. | ||
| 653 | |a Grothendieck-Lefschetz. | ||
| 653 | |a Weil's conjecture. | ||
| 653 | |a Weill's conjecture. | ||
| 653 | |a affine group. | ||
| 653 | |a algebraic geometry. | ||
| 653 | |a algebraic topology. | ||
| 653 | |a analogue. | ||
| 653 | |a cohomology. | ||
| 653 | |a continuous Künneth decomposition. | ||
| 653 | |a factorization homology. | ||
| 653 | |a function fields. | ||
| 653 | |a global "ient stacks. | ||
| 653 | |a infinity. | ||
| 653 | |a local-to-global principle. | ||
| 653 | |a moduli stack. | ||
| 653 | |a number theory. | ||
| 653 | |a rational functions. | ||
| 653 | |a sheaves. | ||
| 653 | |a trace formula. | ||
| 653 | |a triangulated category. | ||
| 700 | 1 | |a Lurie, Jacob, |d 1977- |e author. | |
| 830 | 0 | |a Annals of mathematics studies ; |v no. 199. | |
| 856 | 4 | 0 | |u https://jstor.uam.elogim.com/stable/10.2307/j.ctv4v32qc |z Texto completo |
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