3 problems

Assume that $k$ is a perfect field of characteristic $p>2$, let $m,n,r\in\mathbb{N}$, and write $GL(m|n)_1$ for the first Frobenius kernel of the general linear supergroup scheme.…

Suppose $k$ is algebraically closed. Let $G$ be a height-$1$ infinitesimal unipotent $k$-supergroup scheme, let $M$ be a finite-dimensional rational $G$-supermodule, and let…

Let $k$ be algebraically closed, and let $G$ be an infinitesimal unipotent $k$-supergroup scheme of height $\leq r$. Let $H(G,k)$ denote the cohomology algebra, let…