The differential Galois group of the maximal prounipotent extension is free

Detecting Fast solvability of equations via small powerful Galois groups

Fix an odd prime $p$, and let $F$ be a field containing a primitive $p$th root of unity. It is known that a $p$-rigid field $F$ is characterized by the property that the Galois group $G_F(p)$ of the maximal $p$-extension $F(p)/F$ is a solvable group. We give a new characterization of $p$-rigidity which says that a field $F$ is $p$-rigid precisely when two fundamental canonical quotients of the absolute Galois groups coincide. This condition is further related to analytic $p$-adic groups and to some Galois modules. When $F$ is $p$-rigid, we also show that it is possible to solve for the roots o…

关于 Kähler 微分的计算以及具有独立缺陷的 Galois 扩张的刻画

On the computation of Kähler differentials and characterizations of Galois extensions with independent defect

本文计算赋值环扩张的 Kähler 微分、零化子与 Dedekind 差，并据此利用分歧理想、微分和迹刻画素数次 Galois 扩张中的独立缺陷。