Timeline for the algebraic closure of strict henselian DVR

8 events

when toggle format	what		by	license	comment
Jun 8, 2018 at 9:14	comment	added	Will Sawin		@zzy You are right, I have never once in my life remembered the name "Krasner's lemma".
Jun 7, 2018 at 23:29	comment	added	Zhiyu		Thank you, what you say looks like Krasner's lemma. Before I found something related in the tilting approach to the proof of Fontaine-Winterberger theorem while he didn't give a proof and I come across this problem while searching on mathoverflow.
Jun 6, 2018 at 21:43	comment	added	Will Sawin		@zzy I think always yes. The main thing to check is that every algebraic extension of $K(\hat{A})$ is defined over $K(A)$. To do that, you want to check that if you perturb the coefficients of the defining equation slightly, you get the same Galois extension. This is some famous theorem.
Jun 6, 2018 at 9:35	comment	added	Zhiyu		Do $K(A)$ and $K(\hat A)$ have isomorphic absolute Galois groups?
May 21, 2012 at 3:57	history	edited	Will Sawin	CC BY-SA 3.0	added 2 characters in body
May 20, 2012 at 6:40	history	edited	Will Sawin	CC BY-SA 3.0	added 34 characters in body
May 20, 2012 at 6:23	history	edited	Will Sawin	CC BY-SA 3.0	added 9 characters in body
May 20, 2012 at 5:57	history	answered	Will Sawin	CC BY-SA 3.0