Connected components of moduli stacks of torsors via Tamagawa numbers
K. Behrend, A. Dhillon
Abstract
Let X be a smooth projective geometrically connected curve over a finite field with function field K. Let be a connected semisimple group scheme over X. Under certain hypothesis we prove the equality of two numbers associated with . 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 -torsors on X.
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