## Nagoya Mathematical Journal

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

#### Abstract

We consider the following conjecture: if $X$ is a smooth and irreducible $n$-dimensional projective variety over a field $k$ 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 $H^{n}(X_{s},\mathcal {O}_{X_{s}})$ is bijective. There is another conjecture relating certain invariants of singularities in characteristic zero (the multiplier ideals) with invariants in positive characteristic (the test ideals). We prove that the former conjecture implies the latter one in the case of ambient nonsingular varieties.

#### Article information

Source
Nagoya Math. J., Volume 204 (2011), 125-157.

Dates
First available in Project Euclid: 5 December 2011

https://projecteuclid.org/euclid.nmj/1323107839

Digital Object Identifier
doi:10.1215/00277630-1431849

Mathematical Reviews number (MathSciNet)
MR2863367

Zentralblatt MATH identifier
1239.14011

#### Citation

Mustaţă, Mircea; Srinivas, Vasudevan. Ordinary varieties and the comparison between multiplier ideals and test ideals. Nagoya Math. J. 204 (2011), 125--157. doi:10.1215/00277630-1431849. https://projecteuclid.org/euclid.nmj/1323107839

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