The mapping cone of an Eisenbud operator and applications to exact zero divisors

2024/03/19 by Liana M. Şega, Şega, Liana M., Deepak Sireeshan +1 · 1 citation
Mathematics · #Advanced Topics in Algebra #Algebraic and Geometric Analysis #Commutative Algebra (math.AC) #FOS: Mathematics #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.2403.12458

openalex publication_date 2024/03/19 · openalex created_date 2024/03/21 · openalex updated_date 2026/07/28

Abstract

Let (Q,\mathfrakm,\sf k) be a local ring that admits an exact pair of zero divisors (f,g), M a Q-module with fM = 0 and U a free resolution of M over Q. We construct a degree -2 chain map, which we call an Einsenbud operator, on the complex U ⊗_Q Q/(f,g) and use the mapping cone of the operator to study two exact sequences that relate homology over Q to homology over Q/(f). Several applications are given.

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