Ext modules related to syzygies of the residue field

2023/04/06 by Yuya Otake, Otake, Yuya
Mathematics · #13D02 #13D07 #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #Commutative Algebra (math.AC) #FOS: Mathematics #Finite Group Theory Research #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.2304.02900

openalex publication_date 2023/04/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let R be a commutative noetherian ring. In this paper, we find out close relationships between the module M being embedded in a module of projective dimension at most n and the (n+1)-torsionfreeness of the nth syzygy of M. As an application, when R is local with residue field k, we compute the dimensions as k-vector spaces of Ext modules related to syzygies of k.

Related

• When are n-syzygy modules n-torsionfree?
• Direct summands of syzygy modules of the residue class field
• Asymptotic behavior of dimensions of syzygies
• Syzygy modules with semidualizing or G-projective summands
• Rigidity of Ext and Tor with coefficients in residue fields of a\n commutative noetherian ring