Pulling back Cartier structures along regular maps

Abstract

We introduce a framework for pulling back Cartier modules and their associated invariants along regular $F$-finite morphisms. To achieve this, we construct a relative Cartier isomorphism and operator for an arbitrary regular $F$-finite map of locally noetherian schemes. As an application, we obtain new results on the constancy regions of mixed test ideals, based on the work of Felipe Pérez.

31 pages, 1 figure, we acknowledge the recent work of Daichi Takeuchi (arXiv:2604.14584), few typos fixed, last section shortened, comments are welcome