Gubler, Walter and Jell, Philipp and Kunnemann, Klaus and Martin, Florent and Burgos Gil, Jose Ignacio and Sombra, Martin (2019) CONTINUITY OF PLURISUBHARMONIC ENVELOPES IN NON-ARCHIMEDEAN GEOMETRY AND TEST IDEALS. ANNALES DE L INSTITUT FOURIER, 69 (5). pp. 2331-2376. ISSN 0373-0956, 1777-5310
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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 assumption that X is a surface defined geometrically over the function field of a curve over a perfect field k of positive characteristic. The second case holds in higher dimensions if we assume resolution of singularities over k. The proof follows a strategy from Boucksom, Favre and Jonsson, replacing multiplier ideals by test ideals. Finally, the appendix by Burgos and Sombra provides an example of a semipositive metric whose retraction is not semipositive. The example is based on the construction of a toric variety which has two SNC-models which induce the same skeleton but different retraction maps.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | ANALYTIC SPACES; UNIFORMIZATION; REDUCTION; THEOREM; pluripotential theory; non-archimedean geometry; test ideals |
| Subjects: | 500 Science > 510 Mathematics |
| Divisions: | Mathematics > Prof. Dr. Klaus Künnemann Mathematics > Prof. Dr. Walter Gubler |
| Depositing User: | Dr. Gernot Deinzer |
| Date Deposited: | 27 Apr 2020 09:37 |
| Last Modified: | 27 Apr 2020 09:37 |
| URI: | https://pred.uni-regensburg.de/id/eprint/27775 |
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