Related papers: Fonctions d'une variable $p$-adique et repr\'esent…

We give a direct approach to recover some of the results of Wiles and Tayor on modularity of certain 2-dimensional p-adic representations of the absolute Galois group of Q.

Let $F$ be a finite extension of $Q_p$, $p>2$. We construct admissible unitary completions of certain representations of $GL_2(F)$ on $L$-vector spaces, where $L$ is a finite extension of $F$. When $F=Q_p$ using the results of Berger,…

In this note, we verify that several fundamental results from the theory of representations of reductive $p$-adic groups, extend to finite central extensions of these groups.

Using $p$-adic local Langlands correspondence for $\operatorname{GL}_2(\mathbb{Q}_p)$, we prove that the support of patched modules constructed by Caraiani, Emerton, Gee, Geraghty, Paskunas, and Shin meet every irreducible component of the…

We propose in this paper an approach to Breuil's conjecture on a Langlands correspondence between $p$-adic Galois representations and representations of $p$-adic Lie groups in $p$-adic topological vector spaces. We suggest that Berthelot's…

Let $K$ be an imaginary quadratic field, with associated quadratic character $\alpha$. We construct an analytic $p$-adic $L$-function interpolating the twisted adjoint $L$-values $L(1, \mathrm{ad}(f) \otimes \alpha)$ as $f$ varies in a Hida…

The principal aim of this article is to attach and study $p$-adic $L$-functions to cohomological cuspidal automorphic representations $\Pi$ of $\mathrm{GL}(2n)$ over a totally real field $F$ admitting a Shalika model. We use a modular…

We prove an interpolation formula for the values of certain $p$-adic Rankin--Selberg $L$-functions associated to non-ordinary modular forms.

The Lie superalgebra q(2) and its class of irreducible representations V_p of dimension 2p (p being a positive integer) are considered. The action of the q(2) generators on a basis of V_p is given explicitly, and from here two realizations…

In this thesis, two $\bar{\mathbb{Q}}_\ell$-local systems, $\vphantom{\mathcal{E}}^\circ \mathcal{E}$ and $\vphantom{E}^\circ \mathcal{E}^\prime$ on the regular unipotent subvariety $\mathcal{U}_{0,K}$ of $p$-adic $\operatorname{SL}_2(K)$…

This note studies, and partially solves, 3 elementary questions about continuous rational functions on real (and p-adic) algebraic varieties: Can one restrict such a function to a subvariety? Can one extend such a function from a…

We prove that an admissible $p$-adic Banach representation of $\text{GL}_2K$ whose locally analytic vectors have an infinitesimal character has Gelfand-Kirillov dimension $\leq[K\colon\mathbf Q_p]$, where $p>2$ and $K$ is a $p$-adic field.…

Inspired by several alternative definitions of continued fraction expansions for elements in $\mathbb Q_p$, we study $p$-adically convergent periodic continued fractions with partial quotients in $\mathbb Z[1/p]$. To this end, following a…

In this we give a detailed proof of fermionic p-adic q-measures on Z_p and we will treat some interesting formulae related q-extension of Euler numbers and polynomials.

We provide an introduction to the theory of Eisenstein series and automorphic forms on real simple Lie groups G, emphasising the role of representation theory. It is useful to take a slightly wider view and define all objects over the…

We explore generalizations of the $p$-adic Simpson correspondence on smooth proper rigid spaces to principal bundles under rigid group varieties $G$. For commutative $G$, we prove that such a correspondence exists if and only if the Lie…

We consider the construction of Lagrangians that might be suitable for describing the entire $p$-adic sector of an adelic open scalar string. These Lagrangians are constructed using the Lagrangian for $p$-adic strings with an arbitrary…

The purpose of this paper is to formulate and study a common refinement of a version of Stark's conjecture and its $p$-adic analogue, in terms of Fontaine's $p$-adic period ring and $p$-adic Hodge theory. We construct period-ring-valued…

This note replaces two earlier preprints (1101.3737 by Koll\'ar) and (1211.6681 by Nowak). It studies, and partially solves, 3 elementary questions about continuous rational functions on real (and p-adic) algebraic varieties: Can one…

In this article we put a very elaborate PSH-like structure on the $R_{+}(-)$ groups of products of finite general linear groups. This is not the case we want. Firstly one would really want the actual big PSH algebra of products of general…