Non-Archimedean metric extension for semipositive line bundles

Abstract

For a projective variety $X$ defined over a non-Archimedean complete non-trivially valued field $k$, and a semipositive metrized line bundle $(L,\varphi )$ over it, we establish a metric extension result for sections of $L^{\otimes n}$ from a sub-variety $Y$ to $X$. We form normed section algebras from $(L,\varphi )$ and study their Berkovich spectra. To compare the supremum algebra norm and the quotient algebra norm on the restricted section algebra $V(L_{X|Y})$, two different methods are used: one exploits the holomorphic convexity of the spectrum, following an argument of Grauert; another relies on finiteness properties of affinoid algebra norms.

39 pages, 1 figure

References in corpus (1)

• Métriques de sous-quotient et théorème de Hilbert-Samuel arithmétique pour les faisceaux cohérents