On the stack of semistable G-bundles over an elliptic curve
On the stack of semistable G-bundles over an elliptic curve
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在椭圆曲线上的半稳定 G 丛堆叠上
DOI：
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发表时间：
2014
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通讯作者：
D. Frățilă
中科院分区：
文献类型：
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作者：
D. Frățilă
在最近的一篇论文中，Ben-Zvi 和 Nadler 证明了椭圆曲线上从 0 度 B 丛到 0 度半稳定 G 丛的归纳图是一个小图，伽罗瓦群同构于 G 的 Weyl 群。我们将他们的结果推广到任意还原群 G 的 $${ ext {Bun}}_G$$BunG 的所有连通分量。我们证明对于每个度（即拓扑类型）存在一个独特的抛物线子群，使得该度数的任何半稳定 G 丛都有约简，而且相对于 Levi 的 Weyl 群，归纳图很小。这提供了简单自同构滑轮的新例子，它们是平凡局部系统的爱森斯坦滑轮的组成部分。
In a recent paper Ben-Zvi and Nadler proved that the induction map from B-bundles of degree 0 to semistable G-bundles of degree 0 over an elliptic curve is a small map with Galois group isomorphic to the Weyl group of G. We generalize their result to all connected components of $${ ext {Bun}}_G$$BunG for an arbitrary reductive group G. We prove that for every degree (i.e. topological type) there exists a unique parabolic subgroup such that any semistable G-bundle of this degree has a reduction to it and moreover the induction map is small with Galois group the relative Weyl group of the Levi. This provides new examples of simple automorphic sheaves which are constituents of Eisenstein sheaves for the trivial local system.