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arXiv · 2307.14095

Extension of relative rigid homomorphisms from the formal multiplicative group

Martin Orr
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Abstract

A theorem of L\"utkebohmert 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.

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Martin Orr. 2023-07-26. Extension of relative rigid homomorphisms from the formal multiplicative group. https://arxiv.org/abs/2307.14095

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