Timeline for Completion of a local ring of an arithmetic surface

11 events

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Jun 24, 2019 at 4:28	comment	added	Angelo		The local rings that you describe are all regular, so any arithmetic surface that is not regular can not have this form. In general you get complete locar rings of the form $R[[S,T]]/(ST-\pi^n)$ for some $n \ge 0$.
Jun 23, 2019 at 20:39	history	edited	nowhere dense	CC BY-SA 4.0	added 214 characters in body
Dec 27, 2018 at 21:27	history	edited	nowhere dense	CC BY-SA 4.0	edited title
Dec 21, 2018 at 12:10	history	edited	nowhere dense	CC BY-SA 4.0	added 133 characters in body
Dec 21, 2018 at 10:52	history	edited	nowhere dense	CC BY-SA 4.0	deleted 31 characters in body
Dec 20, 2018 at 21:16	history	edited	YCor		edited tags
Dec 20, 2018 at 21:11	history	edited	nowhere dense	CC BY-SA 4.0	added 126 characters in body
Dec 20, 2018 at 21:09	comment	added	nowhere dense		@JasonStarr oh I see. So I think in order to have a chance to be true we should at least ask for $k$ to be algebraically closed (or maybe just $x$ a rational point). I will add this hypothesis to the question as it is still useful with that for me.
Dec 20, 2018 at 21:05	comment	added	Jason Starr		Welcome new contributor. That is false. For instance, the residue field of $\mathcal{O}_{X,x}$ may be a nontrivial extension of the residue field of $R$.
Dec 20, 2018 at 21:05	review	First posts
Dec 20, 2018 at 21:08
Dec 20, 2018 at 21:02	history	asked	nowhere dense	CC BY-SA 4.0