On the Berkovich double residue fields and birational models
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2020
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866929427781255168 |
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| author | Goto, Keita |
| author_facet | Goto, Keita |
| contents | Just as a residue field can be considered for a point of an algebraic variety, we can also consider a residue field for a point of a Berkovich analytic space. This residue field is a valuation field in the algebraic sense. Then we can consider its residue field as a valuation field. We call it the Berkovich double residue field at the point. In this paper, we consider a point $x$ of the Berkovich analytification of an algebraic variety and identify the Berkovich double residue field at $x$ with the union of the residue fields at the center of $x$ in birational models. Besides, we concretely compute the Berkovich double residue field for any quasi monomial valuation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2007_03610 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | On the Berkovich double residue fields and birational models Goto, Keita Algebraic Geometry Just as a residue field can be considered for a point of an algebraic variety, we can also consider a residue field for a point of a Berkovich analytic space. This residue field is a valuation field in the algebraic sense. Then we can consider its residue field as a valuation field. We call it the Berkovich double residue field at the point. In this paper, we consider a point $x$ of the Berkovich analytification of an algebraic variety and identify the Berkovich double residue field at $x$ with the union of the residue fields at the center of $x$ in birational models. Besides, we concretely compute the Berkovich double residue field for any quasi monomial valuation. |
| title | On the Berkovich double residue fields and birational models |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2007.03610 |