21
votes
English translation of Borel-Serre, Le théorème de Riemann-Roch?
I have just finished this translation! Here is the TeX source, and here is a (live) PDF. Hopefully there shouldn't be too many mistakes :-)
Edit: due to moving links, it's probably best if I just ...
- 1,109
13
votes
Accepted
Is $h^{0,k}$ a topological invariant?
The answer is no.
There are counterexamples already for surfaces, due to X. Gang and F. Campana (unpublished). The link to Campana's article is here, and the relevant result is
Proposition 0.1 ...
- 66.3k
11
votes
Cohomological base change
Basically, you are asking for a weakening of the hypothesis for semi-continuity to only flatness of the higher direct images of $\mathcal{F}$ rather than flatness of $\mathcal{F}$ itself. This is not ...
- 1,566
1
vote
Reference request: category of sheaves of O-modules with coherent cohomology
As mentioned in the comments, I think SGA 6 is one of the original references for this. More specifically:
[SGA 6, II, Corollaire 2.2.2.1] If $X$ is a Noetherian scheme, then the canonical fully ...
- 1,109
Only top scored, non community-wiki answers of a minimum length are eligible