Line bundles on perfectoid covers: case of good reduction
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arXiv
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| Format: | Preprint |
| Published: |
2021
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| _version_ | 1866912128870383616 |
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| author | Heuer, Ben |
| author_facet | Heuer, Ben |
| contents | We study Picard groups and Picard functors of perfectoid spaces which are limits of rigid spaces. For sufficiently large covers that are limits of rigid spaces of good reduction, we show that the Picard functor can be represented by the special fibre. We use our results to answer several open questions about Picard groups of perfectoid spaces from the literature, for example we show that these are not always $p$-divisible. Along the way, we construct a "Hodge--Tate spectral sequence for $\mathbb G_m$" of independent interest. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2105_05230 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Line bundles on perfectoid covers: case of good reduction Heuer, Ben Algebraic Geometry Number Theory 14G45, 14C22, 11G10, 14G22 We study Picard groups and Picard functors of perfectoid spaces which are limits of rigid spaces. For sufficiently large covers that are limits of rigid spaces of good reduction, we show that the Picard functor can be represented by the special fibre. We use our results to answer several open questions about Picard groups of perfectoid spaces from the literature, for example we show that these are not always $p$-divisible. Along the way, we construct a "Hodge--Tate spectral sequence for $\mathbb G_m$" of independent interest. |
| title | Line bundles on perfectoid covers: case of good reduction |
| topic | Algebraic Geometry Number Theory 14G45, 14C22, 11G10, 14G22 |
| url | https://arxiv.org/abs/2105.05230 |