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Weil's Conjecture for Function Fields

Dennis Gaitsgory | Jacob Lurie
€90.99
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A01=Dennis Gaitsgory
A01=Jacob Lurie
Algebraic curve
Algebraic topology (object)
Algebraic variety
Analytic function
Analytic torsion
Author_Dennis Gaitsgory
Author_Jacob Lurie
Ball (mathematics)
Cartesian product
Category=PB
Category=PBMW
Cohomology
Cohomology ring
Commutative algebra
Commutative ring
Complex projective space
Computation
Conjecture
Coordinate singularity
Curvature
Differentiable manifold
Differential form
Differential geometry
Differential topology
Dirac equation
Dirac measure
Eigenvalues and eigenvectors
Einstein field equations
eq_isMigrated=1
eq_isMigrated=2
eq_nobargain
Equation
Existential quantification
Exponential map (Lie theory)
Function space
Functor
Gaussian curvature
Gaussian measure
Geometry
Gravitational constant
Hilbert space
Hodge theory
Holomorphic vector bundle
Home range
Homology (mathematics)
Hyperbolic partial differential equation
Intersection homology
Kahler manifold
Lefschetz duality
Lefschetz hyperplane theorem
Likelihood function
Mathematical induction
Mathematical theory
Maxwell's equations
Minkowski space
Multivariate statistics
Nonlinear Schrodinger equation
Partial differential equation
Projective variety
Pseudo-Riemannian manifold
Quantification (science)
Quantum field theory
Quotient space (topology)
Rational number
Renormalization
Requirement
Ricci curvature
Riemann surface
Riemannian geometry
Riemannian manifold
Semisimple algebraic group
Theorem
Theory
Topological manifold
Transcendental number
Variable (mathematics)
Yang-Mills theory

Product details

  • ISBN 9780691182148
  • Dimensions: 155 x 235mm
  • Publication Date: 19 Feb 2019
  • Publisher: Princeton University Press
  • Publication City/Country: US
  • Product Form: Paperback
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Description

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.
About Dennis Gaitsgory | Jacob Lurie
Dennis Gaitsgory is professor of mathematics at Harvard University. He is the coauthor of A Study in Derived Algebraic Geometry. Jacob Lurie is professor of mathematics at Harvard University. He is the author of Higher Topos Theory (Princeton).

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