Rigid ideals in Gorenstein rings of dimension one

TL;DR

This paper explores the conditions under which certain ideals in one-dimensional Gorenstein local rings have trivial first Ext groups, shedding light on their structural properties.

Contribution

It provides new insights into the existence and characteristics of ideals with vanishing Ext^1 in one-dimensional Gorenstein rings.

Findings

Identification of conditions for ideals with Ext^1=0

Characterization of such ideals in Gorenstein rings

Implications for the structure of Gorenstein rings

Abstract

We investigate the existence of ideals $I$ in a one-dimensional Gorenstein local ring $R$ satisfying $\mathrm{Ext}^{1}_{R}(I,I)=0$.