Adjoint test modules along Cohen--Macaulay morphisms

TL;DR

This paper establishes a transformation rule for adjoint test modules along Cohen--Macaulay morphisms between Cohen--Macaulay varieties with $F$-rational fibers, extending Enescu's theorem on $F$-rationality ascent.

Contribution

It provides an effective transformation rule for adjoint test modules in the context of Cohen--Macaulay morphisms with $F$-rational fibers, advancing understanding of $F$-rationality behavior.

Findings

Derived a transformation rule for adjoint test modules

Extended Enescu's theorem on $F$-rationality ascent

Applicable to Cohen--Macaulay varieties with $F$-rational fibers

Abstract

We provide a transformation rule for adjoint test modules along Cohen--Macaulay maps between Cohen--Macaulay varieties that have $F$-rational geometric fibers. This is, in part, an effective version of Enescu's theorem on the ascent of $F$-rationality under local maps with $F$-rational geometric fibers.