Timeline for Are completions stalks under some Grothendieck topology?
Current License: CC BY-SA 2.5
5 events
| when toggle format | what | by | license | comment | |
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| Dec 23, 2010 at 22:10 | comment | added | Qfwfq | I use to heuristically see $\mathrm{Spec}(\mathcal{O}_{X,x})$ as an "intersection of open neighbourhoods of $x$", while $\mathrm{Spec}(\widehat{\mathcal{O}}_{X,x})$ as an "increasing union of closed subsets containing $x$". | |
| Dec 19, 2010 at 6:21 | answer | added | Emerton | timeline score: 20 | |
| Dec 19, 2010 at 5:42 | comment | added | James D. Taylor | That sounds about right. I wonder how Grothendieck thought of these things. Surely it occurred to him that these notions don't work together, and yet that they are analogous... | |
| Dec 19, 2010 at 3:07 | comment | added | Charles Rezk | The stalk of a sheaf $F$ at a point $p$ is always some sort of colimit of sets of sections $F(U)$ -- this is true for any topology with enough points. The completion looks like an (inverse) limit. So the naive answer to your question is no. | |
| Dec 19, 2010 at 1:47 | history | asked | James D. Taylor | CC BY-SA 2.5 |