Timeline for If the Frobenius endomorphism of a characteristic $p$ ring is epimorphic, is it surjective?
Current License: CC BY-SA 4.0
6 events
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Aug 3, 2021 at 9:21 | comment | added | Matthieu Romagny | @Piotr thank you! In fact I think there are many specific cases where one can prove that F is surjective. The general case still eludes me (and I'm not even sure if surjectivity holds). | |
Aug 3, 2021 at 9:18 | comment | added | Matthieu Romagny | @Wojowu yes, I mean an epimorphism of unitary commutative rings. | |
Jul 31, 2021 at 20:44 | comment | added | Piotr Achinger | P.S. I remember that in a normal ring $R$, the kernel of $d:R\to \Omega^1_R$ equals $R^p$, so in this case the answer to your question should be yes. | |
Jul 31, 2021 at 20:33 | comment | added | Piotr Achinger | Interpreting derivations $R\to M$ as homomorphisms $R\to R\oplus M\cdot\varepsilon$, the condition implies that $\Omega^1_R=0$. I don’t know if this observation is useful. | |
Jul 31, 2021 at 20:24 | comment | added | Wojowu | I take it "epimorphism" is meant in categorical sense? Some authors use it for surjective ring homomorphisms. | |
Jul 31, 2021 at 20:20 | history | asked | Matthieu Romagny | CC BY-SA 4.0 |