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arXiv · 2503.01640

Integral closure of 1-dimensional rings

Mohsen Asgharzadeh
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Abstract

We study certain properties of modules over 1-dimensional local integral domains. First, we examine the order of the conductor ideal and its expected relationship with multiplicity. Next, we investigate the reflexivity of certain colength-two ideals. Finally, we consider the freeness problem of the absolute integral closure of a DVR, and connect this to the reflexivity problem of $R^{\frac{1}{p^n}}$.

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Mohsen Asgharzadeh. 2025-03-03. Integral closure of 1-dimensional rings. https://arxiv.org/abs/2503.01640

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