2021/08/27 by Michael DeBellevue, DeBellevue, Michael, Josh Pollitz +1
Mathematics · #13A35 (primary) #13D02 #13D07 #16E45 (secondary) #Advanced Topics in Algebra #Algebraic Geometry and Number Theory #Commutative Algebra (math.AC) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology
paper · pdf · doi:10.48550/arxiv.2108.12512
openalex publication_date 2021/08/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.