Decomposition of local cohomology tables of modules with large E-depth
Abstract
We introduce the notion of E-depth of graded modules over polynomial rings to measure the depth of certain Ext modules. First, we characterize graded modules over polynomial rings with (sufficiently) large E-depth as those modules whose (sufficiently) partial general initial submodules preserve the Hilbert function of local cohomology modules supported at the irrelevant maximal ideal, extending a result of Herzog and Sbarra on sequentially Cohen-Macaulay modules. Second, we describe the cone of local cohomology tables of modules with sufficiently high E-depth, building on previous work of the second author and Smirnov. Finally, we obtain a non-Artinian version of a socle-lemma proved by Kustin and Ulrich.
Keywords
Cite
@article{arxiv.2003.09626,
title = {Decomposition of local cohomology tables of modules with large E-depth},
author = {Giulio Caviglia and Alessandro De Stefani},
journal= {arXiv preprint arXiv:2003.09626},
year = {2020}
}
Comments
23 pages; we corrected some inaccuracies from previous version and performed minor changes