Diamantine Picard functors of rigid spaces
Fuente:
arXiv
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| Format: | Preprint |
| Publié: |
2021
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| _version_ | 1866909397687468032 |
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| author | Heuer, Ben |
| author_facet | Heuer, Ben |
| contents | For a connected smooth proper rigid space $X$ over a perfectoid field extension of $\mathbb Q_p$, we show that the étale Picard functor of $X$ defined on perfectoid test objects is the diamondification of the rigid analytic Picard functor. In particular, it is represented by a rigid analytic group variety if and only if the rigid analytic Picard functor is.
Second, we study the $v$-Picard functor that parametrises line bundles in the finer $v$-topology on the diamond associated to $X$ and relate this to the rigid analytic Picard functor by a geometrisation of the multiplicative Hodge--Tate sequence.
The motivation is an application to the $p$-adic Simpson correspondence, namely our results pave the way towards the first instance of a new moduli theoretic perspective. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2103_16557 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Diamantine Picard functors of rigid spaces Heuer, Ben Algebraic Geometry 14F20, 14G22, 14G45 For a connected smooth proper rigid space $X$ over a perfectoid field extension of $\mathbb Q_p$, we show that the étale Picard functor of $X$ defined on perfectoid test objects is the diamondification of the rigid analytic Picard functor. In particular, it is represented by a rigid analytic group variety if and only if the rigid analytic Picard functor is. Second, we study the $v$-Picard functor that parametrises line bundles in the finer $v$-topology on the diamond associated to $X$ and relate this to the rigid analytic Picard functor by a geometrisation of the multiplicative Hodge--Tate sequence. The motivation is an application to the $p$-adic Simpson correspondence, namely our results pave the way towards the first instance of a new moduli theoretic perspective. |
| title | Diamantine Picard functors of rigid spaces |
| topic | Algebraic Geometry 14F20, 14G22, 14G45 |
| url | https://arxiv.org/abs/2103.16557 |