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arXiv · 1311.6307

Toward a geometric analogue of Dirichlet's unit theorem

Atsushi Moriwaki
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Abstract

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.

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Atsushi Moriwaki. 2013-11-25. Toward a geometric analogue of Dirichlet's unit theorem. https://doi.org/10.1215/21562261-3157748

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