Related papers: Presque $\mathbf{C}_p$-repr\'esentations et $(\phi…

Let $k$ and $N$ be positive integers with $k\ge2$ even. In this paper we give general explicit upper-bounds in terms of $k$ and $N$ from which all the residual representations $\bar{\rho}_{f,\lambda}$ attached to non-CM newforms of weight…

We show that the Galois cohomology groups of $p$-adic representations of a direct power of $\operatorname{Gal}(\overline{\mathbb{Q}_p}/\mathbb{Q}_p)$ can be computed via the generalization of Herr's complex to multivariable…

We give explicit structure of the graded ring of modular forms with respect to Gamma(N) (N=1,2,3,4,5,6,7,8,9,10,12,16,18) and for some other congruence groups. We also study the modular forms of half-integer weight for certain groups.

The first part of this article is devoted to characterizing the cocycles $\alpha$ of a finite group $G$ that give rise to faithful projective representations of $G$. We prove that a $p$-group $G$ admits a faithful irreducible projective…

We study the representation theory of the infinite type A Hecke algebra over a non-archimedean field in the case where the parameter is a pseudo-uniformizer. Specifically, we consider a family of representations, called almost-symmetric,…

This article starts a computational study of congruences of modular forms and modular Galois representations modulo prime powers. Algorithms are described that compute the maximum integer modulo which two monic coprime integral polynomials…

We show that every Finsler module over a $C^*$-algebra has a quasi-representation into the Banach space $\mathbb{B}(\mathscr{H},\mathscr{K})$ of all bounded linear operators between some Hilbert spaces $\mathscr{H}$ and $\mathscr{K}$. We…

We construct a Wach module for the absolutely semi-stable representations the filtered $(\varphi, N)$-module of which satisfies the Griffiths transversality, which happens in particular for ordinary representations. This construction…

In this paper, we study functional approximations where we choose the so-called radial basis function method and more specifically, quasi-interpolation. From the various available approaches to the latter, we form new quasi-Lagrange…

Surveying some of the recent developments on approximate subgroups and super-strong approximation for thin groups, we describe the Bourgain-Gamburd method for establishing spectral gaps for finite groups and the proof of the classification…

For a central division algebra $D$ of dimension $d^2$ over a finite extension $F$ of $\mathbb Q_p$ or of $\mathbb F_p((t))$, a field $R$ of characteristic prime to $p$, and an irreducible smooth $R$-representation $\pi$ of $G=GL_n(D)$, we…

We study relative Wach modules generalising our previous works on this subject. Our main result shows a categorical equivalence between relative Wach modules and lattices inside relative crystalline representations. Using this result, we…

This paper is devoted to establishing the pointwise upper and lower bounds estimates of the gradient of the solutions to a class of general elliptic systems with H\"{o}lder continuous coefficients in a narrow region where the upper and…

Using a self-replicating method, we generalize with a free parameter some Borwein algorithms for the number $\pi$. This generalization includes values of the Gamma function like $\Gamma(1/3)$, $\Gamma(1/4)$ and of course…

We define some rings of power series in several variables, that are attached to a Lubin-Tate formal module. We then give some examples of (\phi,\Gamma)-modules over those rings. They are the global sections of some reflexive sheaves on the…

For a finite group $G$, we denote by $c(G)$, the minimal degree of faithful representation of $G$ by quasi-permutation matrices over the complex field $\mathbb{C}$. For an irreducible character $\chi$ of $G$, the codegree of $\chi$ is…

Roughly speaking, let us say that a map between metric spaces is large scale conformal if it maps packings by large balls to large quasi-balls with limited overlaps. This quasi-isometry invariant notion makes sense for finitely generated…

In this paper, we recover certain known results about the ladder representations of GL(n, Q_p) defined and studied by Lapid, Minguez, and Tadic. We work in the equivalent setting of graded Hecke algebra modules. Using the Arakawa-Suzuki…

We show how to deduce the determination of the maximal abelian extension of $F$, with $[F:{\mathbf Q}_p]<\infty$, from the theory of Lubin-Tate $(\varphi,\Gamma)$-modules.

Direct and inverse approximation theorems are proved in the Besicovitch-Stepanets spaces $B{\mathcal S}^{p}$ of almost periodic functions in terms of the best approximations of functions and their generalized moduli of smoothness.