Continuity of volumes on arithmetic varieties

Details Continuity of volumes on arithmetic varieties Continuity of volumes on arithmetic varieties

2006-12-11

arxiv.org/abs/math/0612269v2

Mathematics

Number Theory

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Scientific paper

We introduce the volume function for hermitian invertible sheaves on an arithmetic variety as an analogue of the geometric volume function. The main result of this paper is the continuity of the arithmetic volume function. As a consequence, we have the arithmetic Hilbert-Samuel formula for a nef hermitian invertible sheaf. We also give another several applications, for example, a generalized Hodge index theorem, an arithmetic Bogomolov-Gieseker's inequality, etc.

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