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Ordinary varieties and the comparison between multiplier ideals and test ideals

Published online by Cambridge University Press:  11 January 2016

Mircea Mustaţă  and
Vasudevan Srinivas
Mircea Mustaţă
Affiliation:
Department of Mathematics, University of Michigan, Ann Arbor, MI 48109, USAmmustata@umich.edu
Vasudevan Srinivas
Affiliation:
School of Mathematics, Tata Institute of Fundamental Research, Colaba, Mumbai 400005, Indiasrinivas@math.tifr.res.in
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Abstract

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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 Xs to positive characteristic such that the action of the Frobenius morphism on Hn(Xs, OXs) 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.

Keywords

13A3514F1814F30
Type
Research Article
Information
Nagoya Mathematical Journal , Volume 204 , December 2011 , pp. 125 - 157
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 2011

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