论文标题
在弯曲的tamcal $ \ Mathcal g $捆绑中
On tamely ramified $\mathcal G$-bundles on curves
论文作者
论文摘要
我们认为，在光滑的投射曲线和下面的托架上，我们考虑了帕哈里奇的bruhat-tits小组计划。如果地面场的特征是零或阳性，但不是太小，并且通用纤维绝对简单且简单地连接，我们表明该组方案可以写成曲线的驯服封面上的还原组方案的不变性。我们将Bruhat-tits组方案下的Torsors与封面上的还原组方案下的Torsors联系起来，这是覆盖组的行动。为此，我们为这种模棱两可的扭转局开发了当地类型的理论。我们还将在Bruhat-tits组方案下的Torsors的模量堆栈与盖上还原组方案下的模棱两可的Torsors联系起来。在附录中，B。Conrad为伴随组的HASSE原理提供了有限常数字段的函数字段的证明。
We consider parahoric Bruhat-Tits group schemes over a smooth projective curve and torsors under them. If the characteristic of the ground field is either zero or positive but not too small and the generic fiber is absolutely simple and simply-connected, we show that such group schemes can be written as invariants of reductive group schemes over a tame cover of the curve. We relate the torsors under the Bruhat-Tits group scheme and torsors under the reductive group scheme over the cover which are equivariant for the action of the covering group. For this, we develop a theory of local types for such equivariant torsors. We also relate the moduli stacks of torsors under the Bruhat-Tits group scheme and equivariant torsors under the reductive group scheme over the cover. In an Appendix, B. Conrad provides a proof of the Hasse principle for adjoint groups over function fields with finite field of constants.
