Timeline for A slick proof (?) of Zariski-Nagata purity in characteristic $p$
Current License: CC BY-SA 3.0
3 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Sep 28, 2017 at 20:38 | comment | added | Lisa S. | Your explanation about $i \ge 2$ is precisely what I was missing, thank you. This clearly explains the inductive reasoning and the importance of the etaleness through the Cartesianness of the diagram that involves the Frobenii. The latter is also the aspect that would fail if we tried to use the same argument to prove the mere flatness of $g$ as in scenario 2. | |
| Sep 28, 2017 at 19:48 | comment | added | nfdc23 | For #2, it is the step of deducing the discriminant divisor is empty (by checking at height-1 points) where etaleness at height-1 primes is used. For #1, the "mystifying formula" is a typo and should read $h \otimes a \mapsto a \varphi_B(h)$ (for clarity about which Frobenius). For $i\ge 2$, the local cohomology coincides with cohomology of the structure sheaf on the open complement of the closed point, where $\varphi_A$ and $\varphi_B$ form a Cartesian diagram by etaleness there, and the formation of cohomology of quasi-coherent sheaves (on qcqs schemes) commutes with flat base change. | |
| Sep 28, 2017 at 18:00 | history | asked | Lisa S. | CC BY-SA 3.0 |