Timeline for Why considering schemes over discrete valuation rings?
Current License: CC BY-SA 3.0
5 events
| when toggle format | what | by | license | comment | |
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| Apr 22, 2016 at 19:57 | comment | added | Georges Elencwajg | @user54268: sorry, I don't understand your comment. How do you define $R$ and what do you pull-back over $R$ ? | |
| Aug 17, 2014 at 0:17 | vote | accept | Li Yutong | ||
| Aug 16, 2014 at 14:39 | comment | added | user54268 | Technically, as you know, the crucial thing is that for any noetherian scheme $B$ and distinct points $s, \eta \in B$ with $s \in \overline{\{\eta\}}$, there exists a map ${\rm{Spec}}(R) \rightarrow B$ for a dvr $R$ such that the closed point goes to $s$ and the generic point goes to $\eta$. Pullback over $R$ encodes these two fibers at the cost of a huge extension of their residue fields (especially at $s$). So for issues about geometric fibers, base as dvr captures a lot. And of course flatness is easy to control over a dvr (such as for schematic closures from the generic fiber, etc.). | |
| Aug 16, 2014 at 14:33 | history | made wiki | Post Made Community Wiki by Donu Arapura | ||
| Aug 16, 2014 at 14:19 | history | answered | Donu Arapura | CC BY-SA 3.0 |