Tamagawa numbers via nonabelian Poincaré duality
نویسنده
چکیده
3 The geometry of Weil’s conjecture for function fields 8 3.1 More on counting problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 3.2 Stacks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 3.3 Trace formulas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
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Connected Components of Moduli Stacks of Torsors via Tamagawa Numbers
LetX be a smooth projective geometrically connected curve over a finite field with function field K. Let G be a connected semisimple group scheme over X . Under certain hypothesis we prove the equality of two numbers associated with G. The first is an arithmetic invariant, its Tamagawa number. The second, is a geometric invariant, the number of connected components of the moduli stack of G-tors...
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