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Weil's Conjecture for Function Fields: Volume I (Annals of Mathematics Studies, 199)

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Weil's Conjecture for Function Fields: Volume I (Annals of Mathematics Studies, 199)

4.85 91,556 ratings · 9,940 reviews
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Overview: 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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Dennis Gaitsgory
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Dennis Gaitsgory writes contemporary fiction and has always been fascinated by character-driven stories. They hold a degree in English Literature and previously worked as an editor before transitioning to writing their own books. Dennis Gaitsgory lives with their spouse and a very vocal rescue cat.

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Karen Cruz
Karen Cruz November 08, 2024
I thoroughly enjoyed the elegance of it. Beautiful writing, though I craved slightly more depth in the lore. Still, undeniably engaging. A wonderful companion for a quiet weekend.
Andrew Brown
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Dorothy Harris May 09, 2025
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A profoundly satisfying read. I became deeply invested in the protagonist's journey. A masterclass in storytelling. I am now a lifelong fan of this author.
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Exceeded all my expectations. The prose is exquisite. It’s accessible yet undeniably sophisticated. I am now a lifelong fan of this author.
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I was completely blown away. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. An absolute must-read for connoisseurs of the genre.
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Masterpiece from start to finish. I adored how the story unfolded. It kept me captivated without sacrificing elegance. An effortless 5 stars.
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Exceeded all my expectations. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. An effortless 5 stars.
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Such a rich narrative. I became deeply invested in the protagonist's journey. A masterclass in storytelling. I am now a lifelong fan of this author.
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A profoundly satisfying read. The author orchestrated a breathtaking finale. Truly a work of art. A true literary gem.
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Exceeded all my expectations. The prose is exquisite. It’s accessible yet undeniably sophisticated. A true literary gem.
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Absolutely brilliant. The prose is exquisite. It’s accessible yet undeniably sophisticated. A true literary gem.
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I thoroughly enjoyed the elegance of it. The protagonist was compelling, though some subplots felt slightly overshadowed. A very distinguished novel.
Deborah Robinson
Deborah Robinson March 24, 2024
A very strong entry. The middle had a deliberate pace, but the climax was phenomenal. A very distinguished novel.
Susan Martin
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I was completely blown away. The prose is exquisite. It’s accessible yet undeniably sophisticated. I will undoubtedly revisit this masterpiece.
Gary Mitchell
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Amanda Hall
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Excellent, though slightly flawed. The middle had a deliberate pace, but the climax was phenomenal. A solid 4 stars from me.
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A highly sophisticated read. The middle had a deliberate pace, but the climax was phenomenal. A very distinguished novel.
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A profoundly satisfying read. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. An absolute must-read for connoisseurs of the genre.
Robert Hernandez
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A very strong entry. A brilliant concept executed with flair. Just a few pacing choices I would change. A solid 4 stars from me.
Emily Collins
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Masterpiece from start to finish. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. I will undoubtedly revisit this masterpiece.
Andrew Edwards
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I thoroughly enjoyed the elegance of it. The middle had a deliberate pace, but the climax was phenomenal. I would highly recommend this to discerning readers.
Jacob Nguyen
Jacob Nguyen July 24, 2024
Such a rich narrative. I adored how the story unfolded. It kept me captivated without sacrificing elegance. An effortless 5 stars.
Deborah Miller
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A highly sophisticated read. The middle had a deliberate pace, but the climax was phenomenal. I would highly recommend this to discerning readers.
Andrew  Davis
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A decent, if standard, experience. It verged on repetitive in the second act. A more concise edit would have served it well. Unlikely to reread, but a reasonable expenditure of time.
Betty Robinson
Betty Robinson October 14, 2025
A highly sophisticated read. Beautiful writing, though I craved slightly more depth in the lore. Still, undeniably engaging. A wonderful companion for a quiet weekend.
Rebecca Hill
Rebecca Hill September 09, 2024
An acceptable diversion. Certain acts were fascinating, while others felt like a slight endeavor to complete. Unlikely to reread, but a reasonable expenditure of time.
Nicholas Hill
Nicholas Hill June 27, 2024
Exceeded all my expectations. The author orchestrated a breathtaking finale. Truly a work of art. An effortless 5 stars.
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Nicholas Cruz November 05, 2024
A profoundly satisfying read. The author orchestrated a breathtaking finale. Truly a work of art. I am now a lifelong fan of this author.
Sandra Martin
Sandra Martin December 14, 2024
Masterpiece from start to finish. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. I am now a lifelong fan of this author.
Deborah Green
Deborah Green December 16, 2024
A highly sophisticated read. It held my rapt attention, even when certain twists were telegraphed. I would highly recommend this to discerning readers.
Sarah Adams
Sarah Adams May 27, 2025
I thoroughly enjoyed the elegance of it. A brilliant concept executed with flair. Just a few pacing choices I would change. A very distinguished novel.
Steven Lee
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Absolutely brilliant. I adored how the story unfolded. It kept me captivated without sacrificing elegance. An effortless 5 stars.
Edward Turner
Edward Turner June 24, 2024
Such a rich narrative. I adored how the story unfolded. It kept me captivated without sacrificing elegance. A true literary gem.
Melissa Nguyen
Melissa Nguyen August 26, 2024
Absolutely brilliant. The author orchestrated a breathtaking finale. Truly a work of art. An absolute must-read for connoisseurs of the genre.
Elizabeth Moore
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Exceeded all my expectations. I adored how the story unfolded. It kept me captivated without sacrificing elegance. A true literary gem.
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Nicholas Gomez September 20, 2025
Honestly one of the most premium reading experiences lately. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. A true literary gem.
Andrew Green
Andrew Green January 06, 2024
Exceeded all my expectations. I became deeply invested in the protagonist's journey. A masterclass in storytelling. I am now a lifelong fan of this author.
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Absolutely brilliant. I became deeply invested in the protagonist's journey. A masterclass in storytelling. Worth every moment spent reading.
Amanda Taylor
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A decent, if standard, experience. The tempo was somewhat languid, and I found my mind wandering. Not poor, simply average. Unlikely to reread, but a reasonable expenditure of time.
Charles Green
Charles Green February 08, 2025
A highly sophisticated read. The protagonist was compelling, though some subplots felt slightly overshadowed. Quite impressive overall.
Ashley Reyes
Ashley Reyes October 31, 2025
I thoroughly enjoyed the elegance of it. The middle had a deliberate pace, but the climax was phenomenal. I would highly recommend this to discerning readers.
Jennifer Moore
Jennifer Moore August 09, 2024
An acceptable diversion. The tempo was somewhat languid, and I found my mind wandering. Not poor, simply average. Suitable if your reading queue is empty.
Joshua Hill
Joshua Hill December 03, 2024
I thoroughly enjoyed the elegance of it. It held my rapt attention, even when certain twists were telegraphed. Quite impressive overall.
Robert Lopez
Robert Lopez August 08, 2025
I was completely blown away. I adored how the story unfolded. It kept me captivated without sacrificing elegance. A true literary gem.
Dorothy Ramirez
Dorothy Ramirez August 15, 2024
A profoundly satisfying read. The prose is exquisite. It’s accessible yet undeniably sophisticated. A true literary gem.
Ashley Reyes
Ashley Reyes August 31, 2025
I was completely blown away. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. I will undoubtedly revisit this masterpiece.
Robert  Davis
Robert Davis August 30, 2025
Masterpiece from start to finish. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. I will undoubtedly revisit this masterpiece.
Dorothy Harris
Dorothy Harris August 17, 2024
Absolutely brilliant. The prose is exquisite. It’s accessible yet undeniably sophisticated. An effortless 5 stars.
Jacob Gomez
Jacob Gomez November 01, 2025
I thoroughly enjoyed the elegance of it. The middle had a deliberate pace, but the climax was phenomenal. A very distinguished novel.
Jessica Smith
Jessica Smith January 02, 2024
It was adequate. The prose was competent, yet the characters lacked the depth I usually seek. Perfectly average.
Deborah Green
Deborah Green April 03, 2025
I thoroughly enjoyed the elegance of it. The middle had a deliberate pace, but the climax was phenomenal. A very distinguished novel.
Laura Flores
Laura Flores August 04, 2024
Excellent, though slightly flawed. The protagonist was compelling, though some subplots felt slightly overshadowed. A solid 4 stars from me.
Deborah Evans
Deborah Evans July 15, 2024
A highly sophisticated read. The middle had a deliberate pace, but the climax was phenomenal. A very distinguished novel.
Sandra Torres
Sandra Torres December 05, 2024
Excellent, though slightly flawed. Beautiful writing, though I craved slightly more depth in the lore. Still, undeniably engaging. A very distinguished novel.
Sandra Williams
Sandra Williams May 11, 2024
Masterpiece from start to finish. I became deeply invested in the protagonist's journey. A masterclass in storytelling. Worth every moment spent reading.
Matthew White
Matthew White November 02, 2024
I was completely blown away. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. Worth every moment spent reading.
Mark Cruz
Mark Cruz May 27, 2024
Absolutely brilliant. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. Worth every moment spent reading.
Mary Gonzalez
Mary Gonzalez September 30, 2024
A very strong entry. The middle had a deliberate pace, but the climax was phenomenal. A solid 4 stars from me.
Daniel Evans
Daniel Evans June 24, 2025
Masterpiece from start to finish. I became deeply invested in the protagonist's journey. A masterclass in storytelling. An absolute must-read for connoisseurs of the genre.
Matthew Smith
Matthew Smith May 03, 2024
A decent, if standard, experience. It possessed moments of brilliance, but the narrative felt slightly disjointed ultimately. Suitable if your reading queue is empty.
Amanda Rivera
Amanda Rivera February 15, 2025
Absolutely brilliant. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. I am now a lifelong fan of this author.
Dorothy Walker
Dorothy Walker October 18, 2024
Exceeded all my expectations. The author orchestrated a breathtaking finale. Truly a work of art. An absolute must-read for connoisseurs of the genre.
William Ramirez
William Ramirez October 09, 2025
Honestly one of the most premium reading experiences lately. The prose is exquisite. It’s accessible yet undeniably sophisticated. I am now a lifelong fan of this author.
Patricia Perez
Patricia Perez May 04, 2025
Absolutely brilliant. The prose is exquisite. It’s accessible yet undeniably sophisticated. I am now a lifelong fan of this author.
Eric Thomas
Eric Thomas February 28, 2024
Took a moment to build, but the payoff was spectacular. The middle had a deliberate pace, but the climax was phenomenal. A solid 4 stars from me.
Jessica Rivera
Jessica Rivera October 09, 2024
A very strong entry. Beautiful writing, though I craved slightly more depth in the lore. Still, undeniably engaging. A very distinguished novel.
Daniel Evans
Daniel Evans October 18, 2024
A profoundly satisfying read. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. I am now a lifelong fan of this author.
Sharon Adams
Sharon Adams January 07, 2025
I was completely blown away. The author orchestrated a breathtaking finale. Truly a work of art. An absolute must-read for connoisseurs of the genre.
George Sanchez
George Sanchez August 10, 2024
Such a rich narrative. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. An absolute must-read for connoisseurs of the genre.
Paul Nguyen
Paul Nguyen December 01, 2025
I find myself somewhat conflicted. It verged on repetitive in the second act. A more concise edit would have served it well. Perhaps more aligned with a different audience's tastes.
Kevin Wilson
Kevin Wilson March 06, 2024
Took a moment to build, but the payoff was spectacular. Beautiful writing, though I craved slightly more depth in the lore. Still, undeniably engaging. Quite impressive overall.
Joshua Phillips
Joshua Phillips April 04, 2024
A profoundly satisfying read. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. An absolute must-read for connoisseurs of the genre.
Joshua Torres
Joshua Torres March 08, 2024
A highly sophisticated read. It held my rapt attention, even when certain twists were telegraphed. A wonderful companion for a quiet weekend.
Sandra Sanchez
Sandra Sanchez May 17, 2024
I was completely blown away. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. Worth every moment spent reading.
Emily King
Emily King February 13, 2025
A profoundly satisfying read. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. An effortless 5 stars.
Brian Collins
Brian Collins November 18, 2025
Excellent, though slightly flawed. The protagonist was compelling, though some subplots felt slightly overshadowed. I would highly recommend this to discerning readers.
Linda Green
Linda Green December 15, 2024
Honestly one of the most premium reading experiences lately. The prose is exquisite. It’s accessible yet undeniably sophisticated. An effortless 5 stars.
Laura Mitchell
Laura Mitchell February 19, 2025
Such a rich narrative. The prose is exquisite. It’s accessible yet undeniably sophisticated. I will undoubtedly revisit this masterpiece.
Michelle Anderson
Michelle Anderson April 11, 2025
Absolutely brilliant. The prose is exquisite. It’s accessible yet undeniably sophisticated. An effortless 5 stars.
Christopher Garcia
Christopher Garcia December 08, 2024
I was completely blown away. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. An effortless 5 stars.
Jessica Allen
Jessica Allen July 11, 2024
I was completely blown away. I adored how the story unfolded. It kept me captivated without sacrificing elegance. I will undoubtedly revisit this masterpiece.
David Johnson
David Johnson April 01, 2025
I was completely blown away. I became deeply invested in the protagonist's journey. A masterclass in storytelling. Worth every moment spent reading.
Ryan Smith
Ryan Smith February 22, 2025
Exceeded all my expectations. The prose is exquisite. It’s accessible yet undeniably sophisticated. Worth every moment spent reading.
Mary Wright
Mary Wright August 31, 2024
Such a rich narrative. The prose is exquisite. It’s accessible yet undeniably sophisticated. Worth every moment spent reading.
Linda Turner
Linda Turner May 16, 2025
Took a moment to build, but the payoff was spectacular. The protagonist was compelling, though some subplots felt slightly overshadowed. A very distinguished novel.
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