Journal of the European Mathematical Society

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Volume 18, Issue 11, 2016, pp. 2545–2578
DOI: 10.4171/JEMS/648

Published online: 2016-10-12

Local cohomology modules supported at determinantal ideals

Gennady Lyubeznik[1], Anurag K. Singh[2] and Uli Walther[3]

(1) University of Minnesota, Minneapolis, USA
(2) University of Utah, Salt Lake City, USA
(3) Purdue University, West Lafayette, USA

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.

Keywords: Determinantal ideals, local cohomology, vanishing theorems, $\mathcal D$-modules, $\mathcal F$-modules

Lyubeznik Gennady, Singh Anurag, Walther Uli: Local cohomology modules supported at determinantal ideals. J. Eur. Math. Soc. 18 (2016), 2545-2578. doi: 10.4171/JEMS/648