Toward a geometric analogue of Dirichlet's unit theorem

Atsushi Moriwaki
2015 Kyoto Journal of Mathematics  
In this note, 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.
doi:10.1215/21562261-3157748 fatcat:zeh6jqacgjernpandndssqvdle