Hodge-Tate stacks and non-abelian $p$-adic Hodge theory of v-perfect complexes on rigid spaces
Abstract
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.
- Publication:
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arXiv e-prints
- Pub Date:
- February 2023
- DOI:
- 10.48550/arXiv.2302.12747
- arXiv:
- arXiv:2302.12747
- Bibcode:
- 2023arXiv230212747A
- Keywords:
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- Mathematics - Algebraic Geometry
- E-Print:
- Improved exposition. The second part has been split off and appears today as a new submission