Local cohomology modules supported at determinantal ideals

TL;DR

This paper investigates the vanishing behavior of local cohomology modules supported at determinantal ideals, providing new computational results and insights into F-modules and D-modules over various rings.

Contribution

It offers novel vanishing results for local cohomology at determinantal ideals and computes these modules over polynomial rings with integer coefficients.

Findings

Vanishing criteria for local cohomology modules at determinantal ideals

Explicit computations of local cohomology over polynomial rings with integer coefficients

Results on F-modules and D-modules related to 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 F-modules and D-modules that are likely to be of independent interest.