On the boundedness of $k$-algebra homomorphisms between $k$-affinoid algebras

Shou Yoshikawa

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arXiv · 2505.18428

On the boundedness of $k$-algebra homomorphisms between $k$-affinoid algebras

Shou Yoshikawa

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Abstract

Let $k$ be a complete non-archimedean non-trivial valued field. In this paper, we investigate whether every $k$-algebra homomorphism between $k$-affinoid algebras is automatically bounded. We show that this property holds if and only if either $|k^\times|^\mathbb{Q} = \mathbb{R}_{>0}$ holds, or $k$ has positive characteristic and is $F$-finite.

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Shou Yoshikawa. 2025-05-23. On the boundedness of $k$-algebra homomorphisms between $k$-affinoid algebras. https://arxiv.org/abs/2505.18428

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