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Let $k$ be a finite field and $k_E:=k((X))$ denote the field of Laurent series over $k$. We define a Frobenius endomorphism on $k_E$ via $f(X)\mapsto f(X^p)$. We choose a lift $\varphi:k_E^{sep}\...

Let $K$ be a finite field, let $n\ge 1$ be an integer and let $G=\mathrm{GL}(n,K)$ be acting linearly on a finite dimensional $K$-vector space $V$. Although $G$ is a reductive group, it is not ...