13 citations · 20 across the 11 of their papers we have counts for
15 papers
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…
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 .
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…
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…
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…
The p-adic local Langlands correspondence for GL_2(Q_p)
Pierre Colmez, Gabriel Dospinescu, Vytautas Paskunas
The p-adic local Langlands correspondence for GL_2(Q_p) is given by an exact functor from unitary Banach representations of GL_2(Q_p) to representations of the absolute Galois grou…
Irreducible components of deformation spaces: wild 2-adic exercises
Pierre Colmez, Gabriel Dospinescu, Vytautas Paskunas
We prove that the irreducible components of the space of framed deformations of the trivial 2-dimensional mod 2 representation of the absolute Galois group of Q_2 are in natural bi…