Toward a geometric analogue of Dirichlet's unit theorem

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.

16 pages

References in corpus (2)

• On positivity and semistability of vector bundles in finite and mixed characteristics
• Adelic divisors on arithmetic varieties

Cited by in corpus (2)

• Positivity of vector bundles on homogeneous varieties
• Algebraic dynamical systems and Dirichlet's unit theorem on arithmetic varieties