Abstract
Let (Q,𝔫,k) be a commutative local Noetherian ring, f1,…,fc a Q-regular sequence in 𝔫, and R=Q∕(f1,…,fc). 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 and Shamash which yields a free resolution of an R-module M over R given one over Q.
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