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.

arXiv comment31 pages, 1 figure, we acknowledge the recent work of Daichi Takeuchi (arXiv:2604.14584), few typos fixed, last section shortened, comments are welcome