Some genericity results over Noetherian rings
Commutative Algebra
2019-10-15 v1
Abstract
Let M be a filtered module. Some properties of elements of M are "generic" in the following sense: (being open/stable) if an element z of M has a property P then any approximation of z has P; (being dense) any element of M is approximated by an element that has P. (Here the approximation is taken in the filtered sense.) \\ Moreover, one can often ensure an approximation with further special properties, e.g. avoiding a prescribed set of submodules. We prove that being a regular sequence is a generic property. As immediate applications we get corollaries on the generic grades of modules, heights of ideals, properties of determinantal ideals, acyclicity of generalized Eagon-Northcott complexes and vanishing of Tor/Ext.
Cite
@article{arxiv.1910.05731,
title = {Some genericity results over Noetherian rings},
author = {Dmitry Kerner},
journal= {arXiv preprint arXiv:1910.05731},
year = {2019}
}