ON THE BEHAVIOR OF TEST IDEALS UNDER FINITE MORPHISMS

By Karl Schwede, Kevin Tucker. 2010

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We derive transformation rules for test ideals and F-singularities under an arbi- trary finite surjective morphism �: Y ! X of normal varieties in prime characteristic p > 0. The main technique is to relate homomorphisms FOX ! OX, such as Frobenius splittings, to homomorphisms FOY ! OY . In the simplest cases, these rules mirror transforma- tion rules for multiplier ideals in characteristic zero. As a corollary, we deduce sufficient conditions which imply that trace is surjective, i.e. TrY=X(��OY ) = OX.

Subfields: Artificial Intelligence, Computational Theory and Mathematics, Geometry and Topology

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