Timeline for morphism of schemes that is closed at topological space level
Current License: CC BY-SA 2.5
4 events
| when toggle format | what | by | license | comment | |
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| Mar 19, 2010 at 13:24 | comment | added | BCnrd | @saurav: your objection overlooks that $E$ is not a random subset, but a constructible one. (Feel free to delete this comment once it makes sense to you.) | |
| Mar 19, 2010 at 13:22 | comment | added | BCnrd | This argument applies verbatim to any finite-type map between Jacobson schemes (EGA IV$_3$, section 10); e.g. finite type schemes over Dedekind domain with infinitely many primes. But since formation of images and intersections don't generally commute in set theory, it seems appropriate to note (at least for this generalization!) that "pass to underlying set of closed points" commutes with images for constructible sets (because non-empty constructible sets in Jacobson schemes have closed points; clearly false for noetherian schemes in general). | |
| Mar 19, 2010 at 13:18 | comment | added | saurav | But $f(E_c)[=f(E\cap X_c)]$ may not be equal to $f(E)_c[=f(E)\cap Y_c]$. To say that $f(E_c)$ is closed in $Y_c$, we probably need this equality. | |
| Mar 19, 2010 at 11:03 | history | answered | Akhil Mathew | CC BY-SA 2.5 |