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arXiv · 2603.27047

Structure of the Components of the Fixed Locus of a Self-Map of the Berkovich Line

Xander Faber·Niladri Patra
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Abstract

We describe the local and global structure of the fixed locus for the action of a rational function on the Berkovich projective line over a complete nontrivially-valued algebraically closed nonarchimedean field. This includes a bound for the number of connected components that is sharp when the residue characteristic is large or zero. The case of small nonzero residue characteristic will be treated in a subsequent article.

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Xander Faber, Niladri Patra. 2026-03-27. Structure of the Components of the Fixed Locus of a Self-Map of the Berkovich Line. https://arxiv.org/abs/2603.27047

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