Timeline for open faithfully flat morphisms are fpqc
Current License: CC BY-SA 2.5
4 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Sep 18, 2010 at 21:07 | vote | accept | Martin Brandenburg | ||
| Sep 18, 2010 at 20:54 | comment | added | solbap | hopefully this answers 1,2; though it's mostly just a re-hash of Liu's answer 1.if $x \not \in U$ then as Liu says just add pick a open affine $U_0$ containing $x$ and replace $U$ with $U \cup U_0$. 2.Any q-compact open $V$ in $Y$ is covered by a finite number of affine opens $V_i$ so $f|_U^{-1}(V)$is covered by the finitely many $f|_U^{-1}(V_i)$ so it suffices to show $f|_U^{-1}(V_i)$ is q-compact; Liu shows $f|_U^{-1}(V_i)$ is covered by a finite number of affines hence quasi-compact. | |
| Sep 18, 2010 at 19:24 | history | edited | Qing Liu | CC BY-SA 2.5 |
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| Sep 18, 2010 at 13:14 | history | answered | Qing Liu | CC BY-SA 2.5 |