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A Witt Nadel vanishing theorem for threefolds

Part of: Surfaces and higher-dimensional varieties Birational geometry

Published online by Cambridge University Press:  13 January 2020

Yusuke Nakamura  and
Hiromu Tanaka
Yusuke Nakamura
Affiliation:
Graduate School of Mathematical Sciences, The University of Tokyo, 3-8-1 Komaba, Meguro-ku, Tokyo 153-8914, Japan email nakamura@ms.u-tokyo.ac.jp
Hiromu Tanaka
Affiliation:
Graduate School of Mathematical Sciences, The University of Tokyo, 3-8-1 Komaba, Meguro-ku, Tokyo 153-8914, Japan email tanaka@ms.u-tokyo.ac.jp
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Abstract

In this paper, we establish a vanishing theorem of Nadel type for the Witt multiplier ideals on threefolds over perfect fields of characteristic larger than five. As an application, if a projective normal threefold over $\mathbb{F}_{q}$ is not klt and its canonical divisor is anti-ample, then the number of the rational points on the klt-locus is divisible by $q$.

Keywords

rational pointsWitt vectorsNadel vanishing theorem

MSC classification

Primary: 14J45: Fano varieties
Secondary: 14E30: Minimal model program (Mori theory, extremal rays)
Type
Research Article
Information
Compositio Mathematica , Volume 156 , Issue 3 , March 2020 , pp. 435 - 475
Copyright
© The Authors 2020

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