Adjoint test modules along Cohen--Macaulay morphisms

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.

arXiv comment8 pages, comments are still welcome; v2: Weakened assumptions from a finite type base over an $F$-finite field to just $F$-finite thanks to recent work of Bhatt et al (2604.20005)