Connected Components of Moduli Stacks of Torsors via Tamagawa Numbers
Connected Components of Moduli Stacks of Torsors via Tamagawa Numbers
复制标题
通过玉川数连接 Moduli 堆栈的 Torsors 组件
DOI：
10.4153/cjm-2009-001-5
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发表时间：
2005
期刊：
影响因子：
--
通讯作者：
A. Dhillon
中科院分区：
文献类型：
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作者：
K. Behrend;A. Dhillon
设$X$是有限域上一条光滑的射影几何连通曲线，函数域为$K$。设$g$是$X上的连通半单群方案。在某些假设下，我们证明了与$g$相关的两个数相等。第一个是算术不变量，它的玉马川数。第二个是几何不变量，即$X$上的$g$-扭模堆叠的连通分支的个数。我们的结果对于研究连通分量是最有用的，因为关于玉马川数的知识已经很多了。
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 hypotheses 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 $X$ . Our results are most useful for studying connected components as much is known about Tamagawa numbers.