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arXiv · 1904.12405

Resolutions of length four which are Differential Graded Algebras

Andrew R. Kustin
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Abstract

Let $P$ be a commutative Noetherian ring and $F$ be a self-dual acyclic complex of finitely generated free $P$-modules. Assume that $F$ has length four and $F_0$ has rank one. We prove that $F$ can be given the structure of a Differential Graded Algebra with Divided Powers; furthermore, the multiplication on $F$ exhibits Poincar\'e duality. This result is already known if $P$ is a local Gorenstein ring and $F$ is a minimal resolution. The purpose of the present paper is to remove the unnecessary hypotheses that $P$ is local, $P$ is Gorenstein, and $F$ is minimal.

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Andrew R. Kustin. 2019-04-29. Resolutions of length four which are Differential Graded Algebras. https://doi.org/10.1216/jca.2020.12.509

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