Timeline for Is an algebraic space over a DVR, whose special fibre and generic fibre are schemes, actually a scheme?
Current License: CC BY-SA 3.0
7 events
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| Nov 28, 2013 at 11:11 | comment | added | Laurent Moret-Bailly | @Heer: the projection $X'\to Y$ is etale, with trivial residue field extension(s) over the closed point of $X$. So yes, the formal completion is $\mathrm{Spf}(\widehat{R'})$. | |
| Nov 13, 2013 at 15:18 | comment | added | Heer | The most confusing thing is the following: a non-scheme algebraic space over a dvr could have a formal completion along special fibre a formal scheme (if this is ture). @Laurent Moret-Bailly | |
| Nov 8, 2013 at 5:51 | comment | added | Heer | I feel very confused about the relation between an algebraic space $X$ over a DVR and its formal completion $\hat{X}$ along the special fibre. Here I suppose that $X$ is not a scheme, and $\hat{X}$ is actually a formal scheme. I would like to have some intuitive understanding. Thank you very much. | |
| Nov 8, 2013 at 5:49 | comment | added | Heer | I think your example is a particular case of the construction in page 10 of Knutson's book. Let me use the same notation as in that book, now: if I take two closed subscheme $T_1$ and $T_2$ with the same underlying topological space of $X$, do we get the same algebraic space $X_1'=X_2'$ ? | |
| Nov 8, 2013 at 5:43 | comment | added | Heer | what is the formal completion of $Y$ along the special fibre? Is it $\mathrm{Spf} \hat{R'}$ | |
| Jul 24, 2013 at 8:49 | vote | accept | Heer | ||
| Jul 24, 2013 at 8:49 | |||||
| Jul 5, 2013 at 12:21 | history | answered | Laurent Moret-Bailly | CC BY-SA 3.0 |