Non-Archimedean metric extension for semipositive line bundles

2019/04/07 by Fang, Yanbo
#Algebraic Geometry (math.AG) #Complex Variables (math.CV) #FOS: Mathematics

paper · doi:10.48550/arxiv.1904.03696

Abstract

For a projective variety X defined over a non-Archimedean complete non-trivially valued field k, and a semipositive metrized line bundle (L, ϕ) over it, we establish a metric extension result for sections of L^{⊗ n} from a sub-variety Y to X. We form normed section algebras from (L, ϕ) 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.

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