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arXiv · 2208.10551

The conjugate uniformization via 1-motives

Sean Howe·Jackson S. Morrow·Peter Wear
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Abstract

We use the $p$-divisible group attached to a 1-motive to generalize the conjugate $p$-adic uniformization of Iovita--Morrow--Zaharescu to arbitrary $p$-adic formal semi-abelian schemes or $p$-divisible groups over the ring of integers in a $p$-adic field. This mirrors a mixed Hodge theory construction of the inverse uniformization map for complex semi-abelian varieties. We also highlight the geometric structure of the target of the conjugate uniformization map, which is an \'{e}tale cover of a negative Banach--Colmez space in the sense of Fargues--Scholze.

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Sean Howe, Jackson S. Morrow, Peter Wear. 2022-08-22. The conjugate uniformization via 1-motives. https://arxiv.org/abs/2208.10551

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