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


Author: Mircea Mustaţă
Journal: Proc. Amer. Math. Soc. 140 (2012), 805-810
MSC (2010): Primary 13A35; Secondary 14F18, 14F30
DOI: https://doi.org/10.1090/S0002-9939-2011-11240-1
Published electronically: August 29, 2011
MathSciNet review: 2869065
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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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Additional Information

Mircea Mustaţă
Affiliation: Department of Mathematics, University of Michigan, Ann Arbor, Michigan 48109
Email: mmustata@umich.edu

DOI: https://doi.org/10.1090/S0002-9939-2011-11240-1
Keywords: Test ideals, multiplier ideals, ordinary variety
Received by editor(s): December 18, 2010
Published electronically: August 29, 2011
Additional Notes: The author was partially supported by NSF grant DMS-0758454 and a Packard Fellowship.
Communicated by: Irena Peeva
Article copyright: © Copyright 2011 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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