Fang, Yanbo and Gubler, Walter and Kuennemann, Klaus (2025) ON THE NON-ARCHIMEDEAN MONGE-AMPÈRE EQUATION IN MIXED CHARACTERISTIC. NAGOYA MATHEMATICAL JOURNAL, 259. pp. 548-561. ISSN 0027-7630, 2152-6842
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Let X be a smooth projective variety over a complete discretely valued field of mixed characteristic. We solve non-Archimedean Monge-Amp & egrave;re equations on X assuming resolution and embedded resolution of singularities. We follow the variational approach of Boucksom, Favre, and Jonsson proving the continuity of the plurisubharmonic envelope of a continuous metric on an ample line bundle on X. We replace the use of multiplier ideals in equicharacteristic zero by the use of perturbation friendly test ideals introduced by Bhatt, Ma, Patakfalvi, Schwede, Tucker, Waldron, and Witaszek building upon previous constructions by Hacon, Lamarche, and Schwede.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | THEOREM; IDEALS; non-archimedean analytic geometry; non-Archimedean Monge-Amp & egrave;re equation; test-ideals in mixed characteristic |
| Subjects: | 500 Science > 510 Mathematics |
| Divisions: | Mathematics > Prof. Dr. Klaus Künnemann Mathematics > Prof. Dr. Walter Gubler |
| Depositing User: | Dr. Gernot Deinzer |
| Date Deposited: | 09 Jun 2026 05:47 |
| Last Modified: | 09 Jun 2026 05:47 |
| URI: | https://pred.uni-regensburg.de/id/eprint/65925 |
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