Timeline for Riemann-Roch for curves over Dedekind domains and base-change for modular forms
Current License: CC BY-SA 3.0
4 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Apr 22, 2016 at 7:38 | comment | added | მამუკა ჯიბლაძე | It would be useful to see this comment promoted to an answer I think | |
| Dec 22, 2015 at 15:15 | comment | added | Lennart Meier | Ah, I see. I check the vanishing in every fiber and then know that the rank of the first cohomology of $\omega^{\otimes k}$ is constant over all fibers - then I apply cohomology and base change to obtain that $R^1f_*\omega^{\otimes k}$ is locally free and hence also zero (for $f\colon \overline{\mathcal{M}}_n \to \mathrm{Spec}\mathbb{Z}[\frac1n]$). Thanks! | |
| Dec 22, 2015 at 14:25 | comment | added | Jason Starr | You should probably read about the semicontinuity theorem and compatibility of cohomology and base change. This is Section 12 of Chapter III of Hartshorne's book. | |
| Dec 22, 2015 at 14:16 | history | asked | Lennart Meier | CC BY-SA 3.0 |