Extension of relative rigid homomorphisms from the formal multiplicative group
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2023
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| _version_ | 1866912054382690304 |
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| author | Orr, Martin |
| author_facet | Orr, Martin |
| contents | A theorem of Lütkebohmert states that a rigid group homomorphism from the formal multiplicative group to a smooth commutative rigid group $G$, with relatively compact image, can be extended to a homomorphism from the rigid multiplicative group to $G$. In this paper, we prove a relative version of this theorem over a geometrically reduced quasi-compact quasi-separated rigid space. The relative theorem is proved under an additional hypothesis that some open relative subgroup of $G$ has good reduction. This theorem is useful for studying rigid uniformisation of abelian or semiabelian varieties in a relative setting. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2307_14095 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Extension of relative rigid homomorphisms from the formal multiplicative group Orr, Martin Algebraic Geometry 14G22, 14L15 A theorem of Lütkebohmert states that a rigid group homomorphism from the formal multiplicative group to a smooth commutative rigid group $G$, with relatively compact image, can be extended to a homomorphism from the rigid multiplicative group to $G$. In this paper, we prove a relative version of this theorem over a geometrically reduced quasi-compact quasi-separated rigid space. The relative theorem is proved under an additional hypothesis that some open relative subgroup of $G$ has good reduction. This theorem is useful for studying rigid uniformisation of abelian or semiabelian varieties in a relative setting. |
| title | Extension of relative rigid homomorphisms from the formal multiplicative group |
| topic | Algebraic Geometry 14G22, 14L15 |
| url | https://arxiv.org/abs/2307.14095 |