• Corpus ID: 239049444

# On the $p$-adic pro-\'etale cohomology of Drinfeld symmetric spaces

@inproceedings{Bosco2021OnT,
title={On the \$p\$-adic pro-\'etale cohomology of Drinfeld symmetric spaces},
author={Guido Bosco},
year={2021}
}
Via the relative fundamental exact sequence of p-adic Hodge theory, we determine the geometric p-adic pro-étale cohomology of the Drinfeld symmetric spaces defined over a p-adic field, thus giving an alternative proof of a theorem of Colmez-Dospinescu-Nizio l. Along the way, we describe, in terms of differential forms, the geometric pro-étale cohomology of the positive de Rham period sheaf on any connected, paracompact, smooth rigid-analytic variety over a p-adic field, and we do it with…
3 Citations
Solid locally analytic representations of $p$-adic Lie groups
• Mathematics
• 2021
We develop the theory of locally analytic representations of compact p-adic Lie groups from the perspective of the theory of condensed mathematics of Clausen and Scholze. As an application, we
The Picard Group of Vertex Affinoids in the First Drinfeld Cover
• James Taylor
• Mathematics
• 2021
Let F be a finite extension of Qp. Let Ω be the Drinfeld upper half plane, and Σ the first Drinfeld cover of Ω. We study the affinoid open subset Σ1v of Σ 1 above a vertex of the Bruhat-Tits tree for
Prismatic cohomology of rigid analytic spaces over de Rham period ring
• Haoyang Guo
• Mathematics
• 2021
Inspired by Bhatt-Scholze [BS19], in this article, we introduce prismatic cohomology for rigid analytic spaces with l.c.i singularities, with coefficients over Fontaine’s de Rham period ring B dR .

## References

SHOWING 1-10 OF 62 REFERENCES
Integral p-adic étale cohomology of Drinfeld symmetric spaces
• Mathematics
• 2019
We compute the integral $p$-adic etale cohomology of Drinfeld symmetric spaces of any dimension. This refines the computation of the rational $p$-adic etale cohomology from
The pro-étale cohomology of Drinfeld's upper half space
We determine the geometric pro-etale cohomology of Drinfeld's upper half space ${\mathcal X}$ over a p-adic field. The strategy is different from the one given by Colmez, Dospinescu and Niziol. It
On the p-adic cohomology of the Lubin-Tate tower
We prove a finiteness result for the p-adic cohomology of the Lubin-Tate tower. For any n>=1 and p-adic field F, this provides a canonical functor from admissible p-adic representations of GL_n(F)
Overconvergent relative de Rham cohomology over the Fargues-Fontaine curve
We explain how to construct a cohomology theory on the category of separated quasi-compact smooth rigid spaces over $\mathbf{C}_p$ (or more general base fields), taking values in the category of
• Mathematics
Inventiones mathematicae
• 2019
We compute the $p$-adic \'etale and the pro-\'etale cohomologies of the Drinfeld half-space of any dimension. The main input is a new comparison theorem for the $p$-adic pro-\'etale cohomology of
The pro-\'etale topology for schemes
• Mathematics
• 2013
We give a new definition of the derived category of constructible $\ell$-adic sheaves on a scheme, which is as simple as the geometric intuition behind them. Moreover, we define a refined fundamental
• Mathematics
• 2015
We describe a new approach to relative p-adic Hodge theory based on systematic use of Witt vector constructions and nonarchimedean analytic geometry in the style of both Berkovich and Huber. We give
On p-adic comparison theorems for rigid analytic varieties, I.
• Mathematics
• 2019
We compute, in a stable range, the arithmetic p-adic etale cohomology of smooth rigid analytic and dagger varieties (without any assumption on the existence of a nice integral model) in terms of
Specializing varieties and their cohomology from characteristic 0 to characteristic 𝑝
• B. Bhatt
• Mathematics
Algebraic Geometry: Salt Lake City 2015
• 2018
We present a semicontinuity result, proven in recent joint work with Morrow and Scholze, relating the mod $p$ singular cohomology of a smooth projective complex algebraic variety X to the de Rham
Syntomic complexes and p-adic nearby cycles
• Mathematics
• 2015
We compute syntomic cohomology of semistable affinoids in terms of cohomology of $$(\varphi ,\Gamma )$$(φ,Γ)-modules which, thanks to work of Fontaine–Herr, Andreatta–Iovita, and Kedlaya–Liu, is