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arXiv · 2501.03442

Trace ideals, conductors, and ideals of finite (phantom) projective dimension

Kaito Kimura
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Abstract

In this paper, we consider whether parameter test ideals, conductors, $F$-ideals, and trace ideals are contained in an ideal whose quotient ring has finite phantom projective dimension (for example, ideals generated by a system of parameters or ideals with finite projective dimension). One of the main results asserts that such inclusions do not exist in quasi-Gorenstein complete local domains. We also provide examples of Cohen-Macaulay local rings with good properties where such inclusions occur, thus answering negatively a question of Huneke-Swanson.

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Kaito Kimura. 2025-01-28. Trace ideals, conductors, and ideals of finite (phantom) projective dimension. https://arxiv.org/abs/2501.03442

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