Compatible ideals in $\mathbb {Q}$-Gorenstein rings
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- by Thomas Polstra and Karl Schwede;
- Proc. Amer. Math. Soc. 151 (2023), 4099-4112
- DOI: https://doi.org/10.1090/proc/16331
- Published electronically: June 30, 2023
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Abstract:
Suppose $R$ is a $F$-finite and $F$-pure $\mathbb {Q}$-Gorenstein local ring of prime characteristic $p>0$. We show that an ideal $I\subseteq R$ is uniformly compatible ideal (with all $p^{-e}$-linear maps) if and only if exists a module finite ring map $R\to S$ such that the ideal $I$ is the sum of images of all $R$-linear maps $S\to R$. In other words, the set of uniformly compatible ideals is exactly the set of trace ideals of finite ring maps.References
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Bibliographic Information
- Thomas Polstra
- Affiliation: Department of Mathematics, University of Alabama, Tuscaloosa, Alabama 35401
- ORCID: 0000-0003-0856-9296
- Email: tmpolstra@ua.edu
- Karl Schwede
- Affiliation: Department of Mathematics, University of Utah, Salt Lake City, Utah 84102
- MR Author ID: 773868
- Email: schwede@math.utah.edu
- Received by editor(s): April 25, 2022
- Received by editor(s) in revised form: October 17, 2022
- Published electronically: June 30, 2023
- Additional Notes: The first author was supported in part by NSF Postdoctoral Research Fellowship DMS $\#1703856$, NSF Grant DMS #101890, and a grant from the Simons Foundation, Grant Number 814268, MSRI
The second author was supported in part by NSF CAREER Grant DMS #1252860/1501102, NSF Grants #1801849, #1952522, #2101800 and a Simons Fellowship. - Communicated by: Claudia Polini
- © Copyright 2023 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 151 (2023), 4099-4112
- MSC (2020): Primary 13A35
- DOI: https://doi.org/10.1090/proc/16331
- MathSciNet review: 4643305