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I've tried posting this question on MSE, but didn't manage to get an answer there, so I'm trying again here. Sorry in advance if this question is trivial or trivially false. I haven't managed to find ...

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}\...

I'm looking for references for the following statements, which I believe are true: Let $G$ be a simply connected simple linear algebraic group over a finite field $k$ of cardinality $q\ge 4$. Let $Z\...

I'm interested in finding all groups for which the group operation (and inverse map) may be implemented using finite field arithmetic. I've done some searching and have come across "algebraic groups",...