Kyoto Journal of Mathematics

Toward a geometric analogue of Dirichlet’s unit theorem

Atsushi Moriwaki

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In this article, we propose a geometric analogue of Dirichlet’s unit theorem on arithmetic varieties; that is, if X is a normal projective variety over a finite field and D is a pseudo-effective Q-Cartier divisor on X, does it follow that D is Q-effective? We also give affirmative answers on an abelian variety and a projective bundle over a curve.

Article information

Kyoto J. Math., Volume 55, Number 4 (2015), 799-817.

Received: 12 March 2014
Revised: 18 August 2014
Accepted: 18 September 2014
First available in Project Euclid: 25 November 2015

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 14G15: Finite ground fields
Secondary: 11G25: Varieties over finite and local fields [See also 14G15, 14G20] 11R04: Algebraic numbers; rings of algebraic integers

Dirichlet’s unit theorem pseudo-effective divisor finite field


Moriwaki, Atsushi. Toward a geometric analogue of Dirichlet’s unit theorem. Kyoto J. Math. 55 (2015), no. 4, 799--817. doi:10.1215/21562261-3157748.

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