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Dec 20, 2022 at 19:38 comment added Alex Mathers If you have an ring of definition $A_0\subseteq A$ of a Huber ring where $A_0$ has the $x$-adic topology for an element $x$ which is a unit in $A$, then automatically $A=A_0[x^{-1}]$. So in particular this shows it is impossible for $\mathbb Z_p\langle t\rangle$ to be a ring of definition with the $p$-adic topology
Dec 20, 2022 at 16:35 history edited Noam Zimhoni CC BY-SA 4.0
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Dec 20, 2022 at 16:33 comment added Noam Zimhoni Yes, thank you. I'll edit something about it.
Dec 20, 2022 at 16:19 comment added R. van Dobben de Bruyn Of course you can take the $t$-adic valuation (which is trivial when restricted to $\mathbf Q_p$), but I don't think that's what you want, right?
Dec 20, 2022 at 15:21 history asked Noam Zimhoni CC BY-SA 4.0