Journal Article Toward a geometric analogue of Dirichlet’s unit theorem

Moriwaki, Atsushi

55 ( 4 )  , pp.799 - 817 , 2015-12 , Duke University Press
ISSN:2156-2261
NCID:AA12478508
Description
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.
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http://repository.kulib.kyoto-u.ac.jp/dspace/bitstream/2433/207515/1/21562261-3157748.pdf

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