Nagoya Mathematical Journal

Ordinary varieties and the comparison between multiplier ideals and test ideals

Mircea Mustaţă and Vasudevan Srinivas

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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.

Article information

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

First available in Project Euclid: 5 December 2011

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Zentralblatt MATH identifier

Primary: 13A35: Characteristic p methods (Frobenius endomorphism) and reduction to characteristic p; tight closure [See also 13B22]
Secondary: 14F18: Multiplier ideals 14F30: $p$-adic cohomology, crystalline cohomology


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.

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