Ordinary varieties and the comparison between multiplier ideals and test ideals II
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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.References
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Additional Information
- Mircea Mustaţă
- Affiliation: Department of Mathematics, University of Michigan, Ann Arbor, Michigan 48109
- Email: mmustata@umich.edu
- 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
- © Copyright 2011
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - 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
- MathSciNet review: 2869065