On the relative Nullstellensatz in nonarchimedean geometry

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