Connected components of moduli stacks of torsors via Tamagawa numbers

Details Connected components of moduli stacks of torsors via Tamagawa numbers Connected components of moduli stacks of torsors via Tamagawa numbers

2005-03-18

arxiv.org/abs/math/0503383v2

Mathematics

Number Theory

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Scientific paper

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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