Hilbert-Samuel formula and positivity over adelic curves

Huayi Chen, Atsushi Moriwaki

Published 2022-07-05Version 1

We establish, in the setting of Arakelov geometry over adelic curves, an arithmetic Hilbert-Samuel theorem describing the asymptotic behaviour of the metrized graded linear series of an adelic line bundle in terms of its arithmetic intersection number. We then study positivity conditions of adelic line bundles.