Startseite Mathematik Hodge–Tate stacks and non-abelian 𝑝-adic Hodge theory of v-perfect complexes on rigid spaces
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Hodge–Tate stacks and non-abelian 𝑝-adic Hodge theory of v-perfect complexes on rigid spaces

  • Johannes Anschütz ORCID logo EMAIL logo , Ben Heuer ORCID logo und Arthur-César Le Bras ORCID logo
Veröffentlicht/Copyright: 23. Januar 2025

Abstract

Let 𝑋 be a quasi-compact quasi-separated 𝑝-adic formal scheme that is smooth either over a perfectoid 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 and Higgs–Sen modules. This leads to a derived 𝑝-adic Simpson functor.

Award Identifier / Grant number: 444845124

Funding statement: The second author was funded by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) – Project-ID 444845124 – TRR 326.

Acknowledgements

We would like to thank Bhargav Bhatt, Hui Gao, Tongmu He, Juan Esteban Rodríguez Camargo, Peter Scholze, Yupeng Wang, Matti Würthen and Bogdan Zavyalov for helpful discussions. We would like to thank the referee for their close reading and very helpful and detailed comments.

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Received: 2024-01-09
Revised: 2024-11-07
Published Online: 2025-01-23
Published in Print: 2025-03-01

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