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Connected components of moduli stacks of torsors via Tamagawa numbers

K. Behrend·A. Dhillon
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Abstract

Let $X$ 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 $\G$-torsors on $X$.

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K. Behrend, A. Dhillon. 2006-06-13. Connected components of moduli stacks of torsors via Tamagawa numbers. https://arxiv.org/abs/math/0503383

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