Ordinary varieties and the comparison between multiplier ideals and test ideals II

Details Ordinary varieties and the comparison between multiplier ideals and test ideals II Ordinary varieties and the comparison between multiplier ideals and test ideals II

2010-12-14

arxiv.org/abs/1012.2915v2

Mathematics

Commutative Algebra

7 pages; v.2: minor changes, to appear in Proc. Amer. Math. Soc

Scientific paper

We consider the following conjecture: if X is a smooth projective variety over a field of characteristic zero, then there is a dense set of reductions X_s to positive characteristic such that the action of the Frobenius morphism on the top Zariski cohomology of the structure sheaf on X_s is bijective. We also consider the conjecture relating the multiplier ideals of an ideal J on a nonsingular variety in characteristic zero, and the test ideals of the reductions of J to positive characteristic. We prove that the latter conjecture implies the former one. The converse was proved in a joint paper of the author with V. Srinivas.

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