De Aller-Bedste Bøger - over 12 mio. danske og engelske bøger
Levering: 1 - 2 hverdage

Weil's Conjecture for Function Fields

- Volume I (AMS-199)

Bag om 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: WeilΓÇÖs 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 WeilΓÇÖs 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 Γäô-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 WeilΓÇÖs conjecture. The proof of the product formula will appear in a sequel volume.

Vis mere
  • Sprog:
  • Engelsk
  • ISBN:
  • 9780691182148
  • Indbinding:
  • Paperback
  • Sideantal:
  • 320
  • Udgivet:
  • 19. februar 2019
  • Størrelse:
  • 235x156x26 mm.
  • Vægt:
  • 550 g.
  • 8-11 hverdage.
  • 20. november 2024

Normalpris

Abonnementspris

- Rabat på køb af fysiske bøger
- 1 valgfrit digitalt ugeblad
- 20 timers lytning og læsning
- Adgang til 70.000+ titler
- Ingen binding

Abonnementet koster 75 kr./md.
Ingen binding og kan opsiges når som helst.

Beskrivelse af 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: WeilΓÇÖs 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 WeilΓÇÖs 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 Γäô-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 WeilΓÇÖs conjecture. The proof of the product formula will appear in a sequel volume.

Brugerbedømmelser af Weil's Conjecture for Function Fields



Find lignende bøger
Bogen Weil's Conjecture for Function Fields findes i følgende kategorier: