Timeline for The etale site of a closed subscheme and its etale Grothendieck subtopology
Current License: CC BY-SA 2.5
6 events
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| Feb 28, 2011 at 5:34 | comment | added | Jacob Lurie | The original question mentions that given a commutative ring R and an ideal I, two topological spaces (defined using the Zariski topology) are homeomorphic. My answer was addressing the question ``what is an analogous statement for the etale topology?'' (The answer being that you can extract two topoi which are equivalent.) I don't think you can formally deduce anything about defining sites from this. Rather the information would go in the other direction: to write down a proof of my claim, you'll want to think about the problem of lifting etale coverings, as in your earlier reply. | |
| Feb 28, 2011 at 5:21 | comment | added | Anton Geraschenko | Can the topoi really recover this kind of information about the original etale sites? It seems like knowing that $i$ is a closed immersion of etale topoi should prove that the canonical topology on the etale topos of $Y$ is induced by the canonical topology on the etale topos of $X$ (or something like that). | |
| Feb 28, 2011 at 5:08 | comment | added | Anonymous | Thanks for rephrasing it in this language. I'll browse SGA for statement like this tomorrow. | |
| Feb 28, 2011 at 5:08 | history | edited | Jacob Lurie | CC BY-SA 2.5 |
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| Feb 28, 2011 at 5:06 | vote | accept | Anonymous | ||
| Feb 28, 2011 at 5:06 | |||||
| Feb 28, 2011 at 4:54 | history | answered | Jacob Lurie | CC BY-SA 2.5 |