Adic curves: stable reduction, skeletons and metric structure

We study the structure of adic curves over an affinoid field of arbitrary rank. In particular, quite analogously to Berkovich geometry we classify points on curves, prove a semistable reduction theorem in the version of Ducros' triangulations, define associated curve skeletons and prove that th...

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Bibliographic Details
Main Authors Hübner, Katharina, Temkin, Michael
Format Journal Article
LanguageEnglish
Published 11.06.2024
Subjects
Mathematics - Algebraic Geometry
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Summary:We study the structure of adic curves over an affinoid field of arbitrary rank. In particular, quite analogously to Berkovich geometry we classify points on curves, prove a semistable reduction theorem in the version of Ducros' triangulations, define associated curve skeletons and prove that they are deformational retracts in a suitable sense. An important new technical tool is an appropriate compactification of ordered groups that we call the ranger compactification. Intervals of rangers are then used to define metric structures and construct deformational retractions.
DOI:10.48550/arxiv.2406.07414