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arXiv · 2108.12512

A comparison of dg algebra resolutions with prime residual characteristic

Michael DeBellevue·Josh Pollitz
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Abstract

In this article we fix a prime integer $p$ and compare certain dg algebra resolutions over a local ring whose residue field has characteristic $p$. Namely, we show that given a closed surjective map between such algebras there is a precise description for the minimal model in terms of the acyclic closure, and that the latter is a quotient of the former. A first application is that the homotopy Lie algebra of a closed surjective map with residual characteristic $p$ is abelian. We also use these calculations to show deviations enjoy rigidity properties which detect the (quasi-)complete intersection property.

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Michael DeBellevue, Josh Pollitz. 2021-08-27. A comparison of dg algebra resolutions with prime residual characteristic. https://arxiv.org/abs/2108.12512

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