Adic curves: stable reduction, skeletons and metric structure

Fuente: arXiv
Guardado en:
Detalles Bibliográficos
Autores principales: Hübner, Katharina, Temkin, Michael
Formato: Preprint
Publicado: 2024
Materias:
Acceso en línea:
Etiquetas: Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
_version_ 1866917690584596480
author Hübner, Katharina
Temkin, Michael
author_facet Hübner, Katharina
Temkin, Michael
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2406_07414
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle Adic curves: stable reduction, skeletons and metric structure
Hübner, Katharina
Temkin, Michael
Algebraic Geometry
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.
title Adic curves: stable reduction, skeletons and metric structure
topic Algebraic Geometry
url https://arxiv.org/abs/2406.07414