2 problems

Let $K/k$ be a purely inseparable extension of degree $p$, let $X$ be a connected scheme proper over $k$, and let $x_K\in X_K(K)$ lie over $x\in X(k)$. Let $\mathcal{C}_X$ and…

Let $k$ be a field of characteristic $p>5$, and let $\mathbb{A}^1_k$ be the affine line over $k$. Let $\pi^{\rm loc}_A(\mathbb{A}^1_k)$ denote the set of finite local $k$-group sch…