Timeline for Proving Zariski descent
Current License: CC BY-SA 4.0
4 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Oct 26, 2023 at 11:20 | comment | added | Leo Alonso | In any case, this works if the ambient scheme is semi-separated, i.e. intersection of affine opens remain affine. In general (quasi-compact and quasi-separated, say) I doubt this works, one has to use a version of cohomological descent. | |
| Apr 29, 2023 at 6:03 | comment | added | Achim Krause | Ah yes, you're right. Let me think about how to fix this... | |
| Apr 28, 2023 at 19:53 | comment | added | Z. M | I am not sure how the desired descent property follows from this formal argument. Note that the union of two basic affine open subsets is not necessarily affine (let alone being an affine open subset), and I think that this is a special property of the Zariski topology: say, if $x_1+\dots+x_n=1$ for $n>2$, then $D(x_1)$ and $D(x_2+\dots+x_n)$ covers the whole space, and apply the induction hypothesis to $D(x_2+\dots+x_n)$. | |
| Apr 28, 2023 at 18:46 | history | answered | Achim Krause | CC BY-SA 4.0 |