Timeline for Why is $K_{\upsilon}|K$ separable for a global field $K$?

8 events

when toggle format	what		by	license	comment
Dec 29, 2017 at 10:27	review	First posts
Dec 29, 2017 at 10:30
Dec 9, 2017 at 15:30	vote	accept	Frida
Dec 7, 2017 at 1:23	answer	added	Count Dracula		timeline score: 5
Dec 6, 2017 at 21:16	answer	added	nfdc23		timeline score: 5
Dec 6, 2017 at 18:25	history	edited	GH from MO		edited tags
Dec 6, 2017 at 18:13	comment	added	Jason Starr		Also, closely related to this is the fact that an excellent Noetherian local ring that is reduced is analytically reduced, i.e., the completion is also reduced.
Dec 6, 2017 at 18:11	comment	added	Jason Starr		I do not have with me Serre's Local Fields. However, I would just like to point out that for the only positive characteristic global fields, i.e., for finite extensions $K$ of $\mathbb{F}_p(T)$, for every finite extension $L/K$, the integral closure of the DVR $\mathbb{F}_p[T]_{\langle T\rangle}$ in $L$ is finite over the DVR. This is a corollary of the Noether Normalization Theorem. You can find an explicit statement in Eisenbud's Commutative Algebra soon after the proof of the Noether Normalization Theorem.
Dec 6, 2017 at 18:04	history	asked	Frida	CC BY-SA 3.0