Torsion in kernels of induced maps on divisor class groups

TL;DR

This paper studies torsion elements in the kernel of the divisor class group map induced by ideal quotients in local normal domains, extending previous results that focused on principal ideals.

Contribution

It generalizes Griffith-Weston's result from principal ideals to ideals of finite projective dimension, providing new insights into the structure of divisor class groups.

Findings

Identifies conditions under which torsion elements appear in the kernel

Extends known results to a broader class of ideals

Provides a framework for analyzing divisor class groups in local domains

Abstract

We investigate torsion elements in the kernel of the map on divisor class groups of excellent local normal domains A and A/I, for an ideal I of finite projective dimension. The motivation for this work is a result of Griffith-Weston which applies when I is principal.