Strong test ideals associated to Cartier algebras

Abstract

In this note, we use the theory of test ideals and Cartier algebras to examine the interplay between the tight and integral closures in a local ring of positive characteristic. Using work of Schwede, we prove the abundance of strong test ideals, recovering some older fundamental results, and use this approach in concrete computations. In the second part of the paper, the case of Stanley-Reisner rings is fully examined.

The Cartier core map for Cartier algebras

“…This theorem extends existing work on computing certain specific uniformly F -compatible ideals and D-compatible ideals, including the splitting prime and test ideals, for Stanley-Reisner rings [1,3,7,20].…”