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

Shou Yoshikawa

doi:10.48550/arxiv.2505.18428

May 23, 2025Open Access

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

View Full Paper

Ask AI

Bookmark

Share

Key Points

Every k-algebra homomorphism between k-affinoid algebras is bounded under certain conditions.
This boundedness holds if |k×|^Q equals R>0 or if k is F-finite.
Research focuses on complete non-archimedean valued fields, highlighting unique algebraic properties.
Finding has implications for the structure of k-affinoid algebras and their homomorphisms.

Implication

Investigation shows k-algebra homomorphisms are bounded under specific field characteristics.

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^×|Q = R>0 holds, or k has positive characteristic and is F-finite.

Discussion

No takes yet. Share an insight, caveat, or question.

Cite This Study

Shou Yoshikawa (2025) studied this question.

synapsesocial.com/papers/68da58d8c1728099cfd11068 https://doi.org/10.48550/arxiv.2505.18428

View Full Paper

Ask AI

Bookmark

Share

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

Key Points

Implication

Abstract

Discussion

Cite This Study

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

Key Points

Implication

Abstract

Discussion

Cite This Study

Keep reading

Keep reading