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 script D-modules that are likely to be of independent interest.
Bibliographical noteFunding Information:
We thank Bhargav Bhatt, Manuel Blickle, Winfried Bruns, Linquan Ma, Claudia Miller, Claudio Procesi, Matteo Varbaro, and Wenliang Zhang for valuable discussions. G.L. was supported by NSF grant DMS 1161783, A.K.S. by NSF grants DMS 1162585 and DMS 1500613, and U.W. by NSF grants DMS 0901123 and DMS 1401392. G.L. and A.K.S. thank the American Institute of Mathematics for supporting their collaboration. All authors were also supported by NSF grant 0932078000 while in residence at MSRI.
- Determinantal ideals
- Local cohomology
- Script D-modules
- Vanishing theorems