• 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… 
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References

SHOWING 1-10 OF 62 REFERENCES
Integral p-adic étale cohomology of Drinfeld symmetric spaces
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
Cohomology of p-adic Stein spaces
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
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
Relative P-adic Hodge Theory: Foundations
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.
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
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
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