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arXiv · 1811.05508

A converse to a construction of Eisenbud-Shamash

Petter A. Bergh·David A. Jorgensen·W. Frank Moore
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Abstract

Let $(Q,\mathfrak n,k)$ be a commutative local Noetherian ring, $f_1,\dots, f_c$ a $Q$-regular sequence in $\mathfrak n$, and $R=Q/(f_1,\dots,f_c)$. Given a complex of finitely generated free $R$-modules, we give a construction of a complex of finitely generated free $Q$-modules having the same homology. A key application is when the original complex is an $R$-free resolution of a finitely generated $R$-module. In this case our construction is a sort of converse to a construction of Eisenbud-Shamash yielding a free resolution of an $R$-module $M$ over $R$ given one over $Q$.

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Petter A. Bergh, David A. Jorgensen, W. Frank Moore. 2018-11-13. A converse to a construction of Eisenbud-Shamash. https://doi.org/10.1216/jca.2020.12.467

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