Timeline for On the Separability of Certain Extensions of Fields

11 events

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Apr 13, 2017 at 12:58	history	edited	CommunityBot		replaced http://mathoverflow.net/ with https://mathoverflow.net/
Mar 21, 2016 at 16:42	history	edited	David	CC BY-SA 3.0	"made" by "asked"
Aug 4, 2011 at 6:40	history	undeleted	S. Carnahan♦
May 12, 2011 at 23:41	history	deleted	user6930
May 9, 2011 at 6:09	comment	added	David		@Laurent: Thanks for your instructive example. I have made a revision (see below).
May 9, 2011 at 6:08	answer	added	David		timeline score: 2
May 1, 2011 at 10:22	comment	added	Laurent Moret-Bailly		It's the ring of the valuation on $\mathbb{F}_p(t,z^p)$ induced by the $t$-adic valuation on $\mathbb{F}_p((t))$.
May 1, 2011 at 9:51	comment	added	David		Thanks. I'll think about it. Right now I have only a question: (I hope this don't be too obvious, but) why is A a DVR? Why is it actually Noetherian?
May 1, 2011 at 7:43	comment	added	Laurent Moret-Bailly		Something's wrong. There are discrete valuation rings $A$ of char. $p>0$ such that $K(\widehat{A})$ is inseparable over $K(A)$. For instance, choose some $z\in\mathbb{F}_p[[t]]$ which is transcendental over $\mathbb{F}_p(t)$. Then take $A=\mathbb{F}_p[[t]]\cap\mathbb{F}_p(t,z^p)$. Then $A$ is a DVR containing $\mathbb{F}_p[t]$, with completion $\mathbb{F}_p[[t]]$, but we have $z\in\widehat{A}$, $z^p\in A$ and $z\notin K(A)$.
Apr 30, 2011 at 20:07	history	edited	David	CC BY-SA 3.0	deleted 8 characters in body; added 6 characters in body
Apr 30, 2011 at 20:01	history	asked	David	CC BY-SA 3.0