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

Mustaţă, Mircea

doi:10.1090/S0002-9939-2011-11240-1

Ordinary varieties and the comparison between multiplier ideals and test ideals II
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Proc. Amer. Math. Soc. 140 (2012), 805-810 Request permission

Abstract:

We consider the following conjecture: if $X$ is a smooth $n$-dimensional projective variety in characteristic zero, then there is a dense set of reductions $X_s$ to positive characteristic such that the action of the Frobenius morphism on $H^n(X_s,\mathcal {O}_{X_s})$ is bijective. We also consider the conjecture relating the multiplier ideals of an ideal $\mathfrak {a}$ on a nonsingular variety in characteristic zero, and the test ideals of the reductions of $\mathfrak {a}$ to positive characteristic. We prove that the latter conjecture implies the former one.

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