Abhyankars Conjecture and embedding problems
Abhyankars Conjecture and embedding problems
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Abhyankars 猜想和嵌入问题
DOI：
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发表时间：
2003
期刊：
影响因子：
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通讯作者：
D. Harbater
中科院分区：
文献类型：
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作者：
D. Harbater
本文证明了关于特征为p的代数闭域上仿射曲线的基本群的结果，特别是关于嵌入问题和惯性群的结果。证明了这类曲线的Galois覆盖可以通过拟p群扩大其Galois群，并扩大惯性群的p-部分;证明了具有拟p群核的非分歧覆盖的嵌入问题可以通过控制惯性来解决;证明了类似的结果也适用于仿射曲线的光滑分歧覆盖.此外，一个驯服的模拟几何Shafarevich猜想，并简化了以往的结果，包括Abhyankar的猜想一般仿射曲线的证明。部分
This paper proves results concerning the fundamental group of an affine curve over an algebraically closed field of characteristic p, particularly concerning embedding problems and inertia groups. It is shown that Galois covers of such curves can be modified so as to enlarge their Galois groups by quasi-p groups and to enlarge the p-part of inertia groups; that embedding problems for unramified covers with quasi-p group kernel can be solved with control on inertia; and that the analogous result holds for tamely ramified covers of affine curves. In addition, a tame analog of the geometric Shafarevich Conjecture is shown, and simplifications are given for the proofs of previous results including Abhyankar’s Conjecture for general affine curves. Section