3 problems

Let $G$ be a finite group and let a local $G$-action be an embedding $\rho:G\hookrightarrow\operatorname{Aut}(k[[t]])$, where $k$ is algebraically closed of characteristic $p>0$. T…

Let $D_q$ be a dihedral group acting locally over an algebraically closed field $k$ of characteristic $p>0$. Assume that the KGB obstruction for this action vanishes. Dihedral KGB-…

Let $K$ be the ground field, let $X=\mathbb{P}^1_K$, and let $\bar{x}_0$ be the distinguished branch point with residue field $\kappa_0$. For a character…