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Register a new userNon-Archimedean metric extension for semipositive line bundles
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Yanbo Fang
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For a projective variety $X$ defined over a non-Archimedean complete non-trivially valued field $k$, and a semipositive metrized line bundle $(L, phi)$ 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 $(L, phi)$ 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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