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Continuity of Plurisubharmonic Envelopes in Non-Archimedean Geometry and Test Ideals

Gubler, Walter ; Jell, Philipp ; Künnemann, Klaus ; Martin, Florent



Abstract

Let L be an ample line bundle on a smooth projective variety X over a non-archimedean field K. For a continuous metric on L-an, we show in the following two cases that the semipositive envelope is a continuous semipositive metric on L-an and that the non-archimedean Monge-Ampere equation has a solution. First, we prove it for curves using results of Thuillier. Second, we show it under the ...

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