Adic curves: stable reduction, skeletons and metric structure
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arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866917690584596480 |
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| 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 |