most recent 30 from http://mathoverflow.net 2013-06-20T11:22:07Z http://mathoverflow.net/feeds/question/93733 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/93733/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>