46 citations · 67 across the 18 of their papers we have counts for
22 papers
Poincaré duality for pro-étale -local systems
Shizhang Li, Wiesława Nizioł, Emanuel Reinecke +1
We prove finiteness and Poincaré duality for pro-étale -local systems on proper -adic rigid-analytic spaces in the framework of Banach--Colmez spaces and establish…
On the de Rham flip-flopping in dual towers
Gabriel Dospinescu, Wiesława Nizioł
We prove a version of de Rham and Hyodo-Kato flip-flopping for dual towers of rigid analytic spaces including those coming from dual basic local Shimura varieties. The main tool ar…
Hodge Theory of -adic analytic varieties: a survey
Pierre Colmez, Wiesława Nizioł
Hodge Theory of -adic analytic varieties was initiated by Tate in his 1967 paper on -divisible groups, where he conjectured the existence of a Hodge-like decomposition for th…
Topological Vector Spaces
Pierre Colmez, Wiesława Nizioł
Motivated by applications to duality theorems for -adic pro-étale cohomology of rigid analytic spaces, we study the category of Topological Vector Spaces in the setting of conde…
Compactly supported -adic pro-étale cohomology of analytic varieties
Piotr Achinger, Sally Gilles, Wiesława Nizioł
We study properties of compactly supported -adic pro-étale cohomology of smooth partially proper rigid analytic varieties. In particular, we prove a comparison theorem, in a sta…
Duality for -adic geometric pro-étale cohomology
Pierre Colmez, Sally Gilles, Wiesława Nizioł
We prove that -adic geometric pro-étale cohomology of smooth partially proper rigid analytic varieties over -adic fields seen in the category of Topological Vector Spaces sat…
On the geometrization of the -adic local Langlands correspondence
Pierre Colmez, Gabriel Dospinescu, Wiesława Nizioł
We survey results related to our geometrization of a part of the -adic local Langlands correspondence for .
On the -Picard group of Stein spaces
Veronika Ertl, Sally Gilles, Wiesława Nizioł
We study the image of the Hodge-Tate logarithm map (in any cohomological degree), defined by Heuer, in the case of smooth Stein varieties. Heuer, motivated by the computations for…
Arithmetic duality for -adic pro-étale cohomology of analytic curves
Pierre Colmez, Sally Gilles, Wiesława Nizioł
We prove a Poincaré duality for arithmetic -adic pro-étale cohomology of smooth dagger curves over finite extensions of . We deduce it, via the Hochschild-Serre s…
On the cohomology of p-adic analytic spaces, II: The -conjecture
Pierre Colmez, Wiesława Nizioł
Long ago, Fontaine formulated conjectures (now theorems) relating étale and de Rham cohomologies of algebraic varieties over -adic fields. In an earlier work we have shown that…
On the cohomology of -adic analytic spaces, I: The basic comparison theorem
Pierre Colmez, Wiesława Nizioł
The purpose of this paper is to prove a basic -adic comparison theorem for smooth rigid analytic and dagger varieties over the algebraic closure of a -adic field: -adi…
p-adic etale cohomology of period domains
Pierre Colmez, Gabriel Dospinescu, Julien Hauseux +1
We compute the p-torsion and p-adic etale cohomologies with compact support of period domains over local fields in the case of basic isocrystals for quasi-split reductive groups. F…
Integral -adic étale cohomology of Drinfeld symmetric spaces
Pierre Colmez, Gabriel Dospinescu, Wiesława Nizioł
We compute the integral -adic étale cohomology of Drinfeld symmetric spaces of any dimension. This refines the computation of the rational -adic étale cohomology from Colmez-…
On p-adic comparison theorems for rigid analytic varieties, I
Pierre Colmez, Wiesława Nizioł
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 mode…
On uniqueness of -adic period morphisms, II
Wiesława Nizioł
We prove equality of the various -adic period morphisms for smooth, not necessarily proper, schemes. We start with showing that the -theoretical uniqueness criterium we had f…
Cohomology of -adic Stein spaces
Pierre Colmez, Gabriel Dospinescu, Wieslawa Niziol
We compute the -adic étale and the pro-étale cohomologies of the Drinfeld half-space of any dimension. The main input is a new comparison theorem for the -adic pro-étale coho…
On the cohomology of the affine space
Pierre Colmez, Wieslawa Niziol
We compute the p-adic geometric pro-étale cohomology of the affine space (in any dimension). This cohomogy is non-zero, contrary to the étale cohomology, and can be described by me…
On syntomic regulators I: constructions
Wieslawa Niziol
We show that classical Chern classes from higher (-adic) -theory to syntomic cohomology extend to logarithmic syntomic cohomology. These Chern classes are compatible -- in a…
Geometric syntomic cohomology and vector bundles on the Fargues-Fontaine curve
Wieslawa Niziol
We show that geometric syntomic cohomology lifts canonically to the category of Banach-Colmez spaces and study its relation to extensions of modifications of vector bundles on the…
Syntomic cohomology and -adic motivic cohomology
Veronika Ertl, Wieslawa Niziol
We prove a mixed characteristic analog of the Beilinson-Lichtenbaum Conjecture for p-adic motivic cohomology. It gives a description, in the stable range, of p-adic motivic cohomol…
Syntomic complexes and p-adic nearby cycles
Pierre Colmez, Wieslawa Niziol
We compute syntomic cohomology of semistable affinoids in terms of cohomology of -modules which, thanks to work of Fontaine-Herr, Andreatta-Iovita, and Kedlaya-Liu, is known…
Syntomic cohomology and regulators for varieties over p-adic fields
Jan Nekovář, Wiesława Nizioł
We show that the logarithmic version of the syntomic cohomology of Fontaine and Messing for semistable varieties over -adic rings extends uniquely to a cohomology theory for var…