Work

On the Non-archimedean Monge–ampère Equation in Mixed Characteristic

Year: 2025

Type: article

Abstract: 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.

Source: Nagoya Mathematical Journal

DOI: 10.1017/nmj.2025.8

Authors: YANBO FANG, WALTER GUBLER, KLAUS KÜNNEMANN

Institution: University of Regensburg

Language: English

Topic: Algebraic Geometry and Number Theory

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,550

Funder: Deutsche Forschungsgemeinschaft