Local cohomology modules supported at determinantal ideals

Abstract

We provide new results on the vanishing of local cohomology modules supported at ideals of minors of matrices over arbitrary commutative Noetherian rings. In the process, we compute the local cohomology of rings of polynomials with integer coefficients – supported at generic determinantal ideals – and also obtain results on $\mathcal{F}$-modules and $\mathcal{D}$-modules that are likely to be of independent interest.