Let be a commutative local Noetherian ring, a -regular sequence in , and . Given a complex of finitely generated free -modules, we give a construction of a complex of finitely generated free -modules having the same homology. A key application is when the original complex is an -free resolution of a finitely generated -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 -module over given one over .
"A converse to a construction of Eisenbud–Shamash." J. Commut. Algebra 12 (4) 467 - 477, Winter 2020. https://doi.org/10.1216/jca.2020.12.467