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arXiv · 1910.05731

Some genericity results over Noetherian rings

Dmitry Kerner
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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.

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Dmitry Kerner. 2019-10-13. Some genericity results over Noetherian rings. https://arxiv.org/abs/1910.05731

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