Timeline for Definition of etale neighbourhood

6 events

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Apr 17, 2011 at 3:37	comment	added	Mariano Suárez-Álvarez		While you may well be stupid, your user name makes it a bit hard to talk to you seriously... Could you consider something more neutral?
Apr 16, 2011 at 22:19	comment	added	Donu Arapura		It seems our comments crossed.
Apr 16, 2011 at 22:19	comment	added	Donu Arapura		If you look further down the page (p. 38), you'll see that both versions, with and without the condition $k(x)=k(y)$, are considered. If you include it and take the direct limit of regular functions over all etale neighbourhoods you get the Henselization $\mathcal{O}_x^h$. If you do this but drop the condition $k(x)=k(y)$, you get the strict Henselization. (By the way, you want to consider a different alias.)
Apr 16, 2011 at 22:06	comment	added	mephisto		The condition is needed so that when you take the direct limit of the rings $\mathcal{O}(Y)$ over the etale nhds $Y$ of $x$ you get the henselization of the local ring $\mathcal{O}_x$. A more natural notion is the etale nhd of a geometric point, where the direct limit gives the strict henselization.
Apr 16, 2011 at 20:34	history	edited	user14449	CC BY-SA 3.0	deleted 5 characters in body
Apr 16, 2011 at 20:12	history	asked	user14449	CC BY-SA 3.0