On the non-archimedean Monge-Ampère equation in mixed characteristic
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2022
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| _version_ | 1866915660343279616 |
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| author | Fang, Yanbo Gubler, Walter Künnemann, Klaus |
| author_facet | Fang, Yanbo Gubler, Walter Künnemann, Klaus |
| contents | Let X be a smooth projective variety over a complete discretely valued field of mixed characteristic. We solve non-archimedean Monge-Ampère 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2203_12282 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | On the non-archimedean Monge-Ampère equation in mixed characteristic Fang, Yanbo Gubler, Walter Künnemann, Klaus Algebraic Geometry Number Theory Primary 14G22, Secondary 14F18, 32P05, 32U15 Let X be a smooth projective variety over a complete discretely valued field of mixed characteristic. We solve non-archimedean Monge-Ampère 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. |
| title | On the non-archimedean Monge-Ampère equation in mixed characteristic |
| topic | Algebraic Geometry Number Theory Primary 14G22, Secondary 14F18, 32P05, 32U15 |
| url | https://arxiv.org/abs/2203.12282 |