In his previous paper, the author proposed as a problem a purely inseparable analogue of the Abhyankar conjecture for affine curves in positive characteristic and gave a partial answer to it, which includes a complete answer for finite local nilpotent group schemes. In the present paper, motivated by the Abhyankar conjectures with restricted ramifications due to Harbater and Pop, we study a refined version of the analogous problem, based on a recent work on tamely ramified torsors due to Biswas–Borne, which is formulated in terms of root stacks. We study an embedding problem to conclude that the refined analogue is true in the solvable case.

中文翻译：

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有限局部扭量在扭曲曲线上的嵌入问题

在他之前的论文中，作者提出了一个纯不可分的正特性仿射曲线的 Abhyankar 猜想的类比问题，并给出了部分答案，其中包括有限局部幂零群方案的完整答案。在本文中，受由 Harbater 和 Pop 引起的具有限制性分支的 Abhyankar 猜想的启发，我们研究了类似问题的改进版本，基于最近关于 Biswas-Borne 引起的温和分支torors 的工作，该工作是根据以下公式制定的根堆栈。我们研究了一个嵌入问题，以得出结论，在可解决的情况下，精炼的类似物是正确的。