%0 Journal Article
%T On the behavior of test ideals under finite morphisms
%A Karl Schwede
%A Kevin Tucker
%J Mathematics
%D 2010
%I arXiv
%R 10.1090/S1056-3911-2013-00610-4
%X We derive transformation rules for test ideals and $F$-singularities under an arbitrary finite surjective morphism $\pi : Y \to X$ of normal varieties in prime characteristic $p > 0$. The main technique is to relate homomorphisms $F_{*} O_{X} \to O_{X}$, such as Frobenius splittings, to homomorphisms $F_{*} O_{Y} \to O_{Y}$. In the simplest cases, these rules mirror transformation rules for multiplier ideals in characteristic zero. As a corollary, we deduce sufficient conditions which imply that trace is surjective, i.e. $Tr_{Y/X}(\pi_{*}O_{Y}) = O_{X}$.
%U http://arxiv.org/abs/1003.4333v3