If $X$ is a complex algebraic variety stratified by a collection of locally closed subvarieties, the Cousin complex associated to this filtration is a tool to reduce the computation of the cohomology of ${\cal O}_X$-modules on $X$ to the computation of local cohomology groups with supports given by the stratification. When the stratification has nice properties, this reduction happens to be quite useful. In this talk we will use this idea to compute the cohomology of line bundles on horospherical varieties. We will prove the following main tool for these computations: a Künneth-like formula for local cohomology.
This is a joint work in progress with Narasimha Chary Bonala.