Pulling back Cartier structures along regular maps

TL;DR

This paper develops a framework for pulling back Cartier modules along regular $F$-finite maps, introducing a relative Cartier isomorphism, and applies it to study constancy regions of mixed test ideals.

Contribution

It constructs a relative Cartier isomorphism for regular $F$-finite maps and applies it to analyze invariants of Cartier modules under such maps.

Findings

Established a relative Cartier isomorphism for regular $F$-finite maps.

Provided new results on constancy regions of mixed test ideals.

Extended the theory of Cartier modules in the context of regular morphisms.

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 P\'erez.