English

On the relative Nullstellensatz in nonarchimedean geometry

Algebraic Geometry 2025-12-30 v2 Number Theory

Abstract

We establish a relative version of the Nullstellensatz for algebras topologically of finite type over a given Banach Tate ring AA, under the assumption that the corresponding statement holds for rational localizations of AA. This applies in particular to pseudoaffinoid algebras and to the coordinate rings of affinoid subspaces of a Fargues--Fontaine curve.

Keywords

Cite

@article{arxiv.2503.18183,
  title  = {On the relative Nullstellensatz in nonarchimedean geometry},
  author = {Kiran S. Kedlaya and Yutaro Mikami},
  journal= {arXiv preprint arXiv:2503.18183},
  year   = {2025}
}

Comments

9 pages, accepted version, to appear in Research in Number Theory