When are n-syzygy modules n-torsionfree?

2016/04/13 by Hiroki Matsui, Ryo Takahashi, Matsui, Hiroki +3 · 1 citation
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #Commutative Algebra (math.AC) #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.1604.03684

openalex publication_date 2016/04/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let R be a commutative noetherian ring. We consider the question of when n-syzygy modules over R are n-torsionfree in the sense of Auslander and Bridger. Our tools include Serre's condition and certain conditions on the local Gorenstein property of R. Our main result implies the converse of a celebrated theorem of Evans and Griffith.

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• Base change of (Gorenstein) transpose, k-torsionfree modules, and quasi-faithfully flat extensions

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