The relative Hodge-Tate spectral sequence for rigid analytic spaces
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866917580470484992 |
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| author | Heuer, Ben |
| author_facet | Heuer, Ben |
| contents | We construct a relative Hodge-Tate spectral sequence for any smooth proper morphism of rigid analytic spaces over a perfectoid field extension of $\mathbb Q_p$. To this end, we generalise Scholze's strategy in the absolute case by using smoothoid adic spaces. As our main additional ingredient, we prove a perfectoid version of Grothendieck's "cohomology and base-change". We also use this to prove local constancy of Hodge numbers in the rigid analytic setting, and deduce that the relative Hodge-Tate spectral sequence degenerates. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_00842 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The relative Hodge-Tate spectral sequence for rigid analytic spaces Heuer, Ben Algebraic Geometry 14G22, 14F30, 14G45 We construct a relative Hodge-Tate spectral sequence for any smooth proper morphism of rigid analytic spaces over a perfectoid field extension of $\mathbb Q_p$. To this end, we generalise Scholze's strategy in the absolute case by using smoothoid adic spaces. As our main additional ingredient, we prove a perfectoid version of Grothendieck's "cohomology and base-change". We also use this to prove local constancy of Hodge numbers in the rigid analytic setting, and deduce that the relative Hodge-Tate spectral sequence degenerates. |
| title | The relative Hodge-Tate spectral sequence for rigid analytic spaces |
| topic | Algebraic Geometry 14G22, 14F30, 14G45 |
| url | https://arxiv.org/abs/2402.00842 |