User prl - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-25T05:04:35Z http://mathoverflow.net/feeds/user/21671 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/93733/finite-weight-spaces-for-coherent-sheaf-cohomology Finite weight spaces for coherent sheaf cohomology PRL 2012-04-11T03:24:26Z 2012-04-11T03:24:26Z <p>Given a smooth quasiprojective variety $X$ with a coherent sheaf $E$, if $X$ is not projective, then the sheaf cohomology of $E$ may not be finite-dimensional. However, if we also have the action of a torus $T$ on $X$ so that $E$ is equivariant, then the cohomology groups are naturally representations of $T$, and it could be the case that the weight spaces are finite-dimensional. Under what hypotheses will this be true? For instance, if $X$ has proper fixed locus, is that enough? </p> http://mathoverflow.net/questions/93389/direct-limits-and-quasi-isomorphism/93393#93393 Answer by PRL for Direct limits and quasi-isomorphism PRL 2012-04-07T07:25:47Z 2012-04-07T07:25:47Z <p>Doesn't this follow from the exactness of direct limits for modules?</p> http://mathoverflow.net/questions/89361/tame-ramification-and-families-of-curves Tame ramification and families of curves PRL 2012-02-24T03:41:19Z 2012-02-24T03:41:19Z <p>Suppose I have a stable curve $$C \rightarrow \mathrm{Spec} R$$ over a complete DVR which has smooth generic fiber and regular total space. If I look at $N$-torsion of the Jacobian of the generic fiber, this defines a ramified cover of my base. Are there any geometric conditions I can impose on my curve that will give me control on the ramification? For instance, if the Jacobian extends to a proper group scheme over $R$, then there is no ramification. But more generally?</p> http://mathoverflow.net/questions/115191/properties-of-subvarieties-of-a-simple-abelian-variety Comment by PRL PRL 2012-12-02T18:11:34Z 2012-12-02T18:11:34Z In general h^1,0 &gt;= dim A, but that doesn't use the fact that the map is a closed immersion. http://mathoverflow.net/questions/114144/isotrivial-k3-family-and-picard-number/114146#114146 Comment by PRL PRL 2012-11-22T13:01:02Z 2012-11-22T13:01:02Z The result holds more generally even if the base isn't compact; by a result of green, the jumping locus is analytically dense so you can't just remove the points.