The different for base change of arithmetic curves
Fuente:
arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866910917269127168 |
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| author | Waeterschoot, Art |
| author_facet | Waeterschoot, Art |
| contents | We introduce a method for studying reduction types of arithmetic curves and wildly ramified base change. We give new proofs of earlier results of Lorenzini and Obus-Wewers, and resolve a question of Lorenzini on the Euler characteristic of the resolution graph of a $p$-cyclic arithmetic surface quotient singularity. Our method consists of constructing a simultaneous skeleton for the associated cover of Berkovich analytifications and applying a skeletal Riemann-Hurwitz formula. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_16543 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The different for base change of arithmetic curves Waeterschoot, Art Number Theory Algebraic Geometry We introduce a method for studying reduction types of arithmetic curves and wildly ramified base change. We give new proofs of earlier results of Lorenzini and Obus-Wewers, and resolve a question of Lorenzini on the Euler characteristic of the resolution graph of a $p$-cyclic arithmetic surface quotient singularity. Our method consists of constructing a simultaneous skeleton for the associated cover of Berkovich analytifications and applying a skeletal Riemann-Hurwitz formula. |
| title | The different for base change of arithmetic curves |
| topic | Number Theory Algebraic Geometry |
| url | https://arxiv.org/abs/2504.16543 |