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

Source 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 (e.g., 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 and Swanson.