Wildly ramified covers with large genus
Wildly ramified covers with large genus
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具有大属的广泛分枝盖
DOI：
10.1016/j.jnt.2005.10.013
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发表时间：
2005
影响因子：
0.7
通讯作者：
R. Pries
中科院分区：
文献类型：
--
作者：
R. Pries
本文研究了广义分歧G-Galois覆盖：Y→X在B（定义在特征为p的代数闭域上）分支.我们证明了，即使G，X，B和惯性群是固定的，也会出现任意高亏格的曲线Y。证明依赖于覆盖的曲线和正式修补芽伽罗瓦行动。作为推论，我们证明了对任意非平凡拟p群G和任意充分大的整数σ（p ∈ σ），在点∞上存在一个具有导体σ的仿射线的G-Galois tale覆盖.
We study wildly ramified G-Galois covers ϕ:Y→X branched at B (defined over an algebraically closed field of characteristic p). We show that curves Y of arbitrarily high genus occur for such covers even when G, X, B and the inertia groups are fixed. The proof relies on a Galois action on covers of germs of curves and formal patching. As a corollary, we prove that for any nontrivial quasi-p group G and for any sufficiently large integer σ with p∤σ, there exists a G-Galois étale cover of the affine line with conductor σ above the point ∞.