Hodge-Tate stacks and non-abelian $p$-adic Hodge theory of v-perfect complexes on rigid spaces
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866909461533163520 |
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| author | Anschütz, Johannes Heuer, Ben Bras, Arthur-César Le |
| author_facet | Anschütz, Johannes Heuer, Ben Bras, Arthur-César Le |
| contents | Let $X$ be a quasi-compact quasi-separated $p$-adic formal scheme that is smooth either over a perfectoid $\mathbb{Z}_p$-algebra or over some ring of integers of a $p$-adic field. We construct a fully faithful functor from perfect complexes on the Hodge-Tate stack of $X$ up to isogeny to perfect complexes on the v-site of the generic fibre of $X$. Moreover, we describe perfect complexes on the Hodge-Tate stack in terms of certain derived categories of Higgs, resp. Higgs-Sen modules. This leads to a derived $p$-adic Simpson functor. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2302_12747 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Hodge-Tate stacks and non-abelian $p$-adic Hodge theory of v-perfect complexes on rigid spaces Anschütz, Johannes Heuer, Ben Bras, Arthur-César Le Algebraic Geometry Let $X$ be a quasi-compact quasi-separated $p$-adic formal scheme that is smooth either over a perfectoid $\mathbb{Z}_p$-algebra or over some ring of integers of a $p$-adic field. We construct a fully faithful functor from perfect complexes on the Hodge-Tate stack of $X$ up to isogeny to perfect complexes on the v-site of the generic fibre of $X$. Moreover, we describe perfect complexes on the Hodge-Tate stack in terms of certain derived categories of Higgs, resp. Higgs-Sen modules. This leads to a derived $p$-adic Simpson functor. |
| title | Hodge-Tate stacks and non-abelian $p$-adic Hodge theory of v-perfect complexes on rigid spaces |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2302.12747 |