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

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On the relative Nullstellensatz in nonarchimedean geometry

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年3月5日

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  • Kiran S. Kedlaya,
  • Yutaro Mikami

摘要

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.