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MO question 19282 is about integral epimorphisms of commutative rings, and a counterexample is given to surjectivity. What about the case of the Frobenius endomorphism of a commutative, characteristic ...

I was reading Fedder's original paper which proved what is now known as "Fedder's criterion". I noticed that the abstract stated something which is a priori stronger than what is proved in ...

Let $X$ be a connected smooth algebraic variety over a field $k$ of characteristic $p > 0$. We can consider the Frobenius morphism associated to $X \mapsto Spec(k)$. I'd like to show $\Omega^{1}_{X/...

If $ n \in \mathbb{N} $, then $ \mathbb{G}_{m}^{n} $ is linearly reductive. Let $ \beta: \mathbb{G}_{m}^{n} \to \operatorname{GL}(\mathbf{V}) $ where $ \mathbf{V} $ is a vector space over an ...