## Kyoto Journal of Mathematics

### Toward a geometric analogue of Dirichlet’s unit theorem

Atsushi Moriwaki

#### Abstract

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 $\mathbb{Q}$-Cartier divisor on $X$, does it follow that $D$ is $\mathbb{Q}$-effective? We also give affirmative answers on an abelian variety and a projective bundle over a curve.

#### Article information

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

Dates
Revised: 18 August 2014
Accepted: 18 September 2014
First available in Project Euclid: 25 November 2015

https://projecteuclid.org/euclid.kjm/1448460079

Digital Object Identifier
doi:10.1215/21562261-3157748

Mathematical Reviews number (MathSciNet)
MR3479310

Zentralblatt MATH identifier
1349.14094

#### Citation

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. https://projecteuclid.org/euclid.kjm/1448460079

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