In this article, we propose a geometric analogue of Dirichlet’s unit theorem on arithmetic varieties; that is, if is a normal projective variety over a finite field and is a pseudo-effective -Cartier divisor on , does it follow that is -effective? We also give affirmative answers on an abelian variety and a projective bundle over a curve.
"Toward a geometric analogue of Dirichlet’s unit theorem." Kyoto J. Math. 55 (4) 799 - 817, December 2015. https://doi.org/10.1215/21562261-3157748