Related papers: Quasirational relation modules and p-adic Malcev c…

We introduce a notion of c-group, which is a group up to congruence relation and consider the corresponding category. Extensions, actions and crossed modules (c-crossed modules) are defined in this category and the semi-direct product is…

Our aim is to transfer several foundational results from the modular representation theory of finite groups to the wider context of profinite groups. We are thus interested in profinite modules over the completed group algebra k[[G]] of a…

This paper is devoted to the more elementary aspects of the contramodule story, and can be viewed as an extended introduction to the more technically complicated arXiv:1503.05523. Reduced cotorsion abelian groups form an abelian category,…

Given a quaternionic form G of a p-adic classical group (p odd) we classify all cuspidal irreducible representations of G with coefficients in an algebraically closed field of characteristic different from p. We prove two theorems: At…

This thesis aims to serve as an introduction to the theory of quasitilings for amenable groups. In order to showcase the power of this theory, we focus on the study of the Sofic L\"uck Approximation Conjecture, which can be proven for…

Let G be a connected reductive quasisplit algebraic group over a field L which is a finite extension of the p-adic numbers. We construct an exact sequence modelled on (the dual of) the BGG resolution involving locally analytic principal…

In this paper, for any prime $p$, we propose the notion of a $p$-transitive association scheme. This notion aims to generalize the fact that the regular module of a group algebra of a finite group has a unique trivial submodule to the case…

We prove that for any FAb compact $p$-adic analytic group $G$, its representation zeta function is a finite sum of terms $n_{i}^{-s}f_{i}(p^{-s})$, where $n_{i}$ are natural numbers and $f_{i}(t)\in\mathbb{Q}(t)$ are rational functions.…

We wish to use graded structures [KrVu87], [Vu01] on dffierential operators and quasimodular forms on classical groups and show that these structures provide a tool to construct p-adic measures and p-adic L-functions on the corresponding…

Rational discrete cohomology and homology for a totally disconnected locally compact group $G$ is introduced and studied. The $\mathrm{Hom}$-$\otimes$ identities associated to the rational discrete bimodule $\mathrm{Bi}(G)$ allow to…

We introduce new methods from p-adic integration into the study of representation zeta functions associated to compact p-adic analytic groups and arithmetic groups. They allow us to establish that the representation zeta functions of…

We use quasi-orders to describe the structure of C-groups. We do this by associating a quasi-order to each compatible C-relation of a group, and then give the structure of such quasi-ordered groups. We also reformulate in terms of…

Inspired from the work of P. Scholze on the finiteness of \(\mathbf{F}_{p}\)-cohomology groups of proper rigid-analytic varieties over \(p\)-adic fields, Zavyalov recently introduced the notion of almost coherent rings, which plays a key…

We give a complete characterization of pseudovarieties of semigroups whose finitely generated relatively free profinite semigroups are equidivisible. Besides the pseudovarieties of completely simple semigroups, they are precisely the…

Using methods of associative algebras, Lie theory, group cohomology, and modular representation theory, we construct profinite $p$-adic analytic groups such that the centralizer of each of their non-trivial elements is abelian. The paper…

We show that every unitary representation of a solvable discrete virtually nilpotent group G is quasidiagonal. Roughly speaking, this says that every unitary representation of G approximately decomposes as a direct sum of finite dimensional…

Modal probabilistic logics provide a framework for reasoning about probability in modal contexts, involving notions such as knowledge, belief, time, and action. In this paper, we study a particular family of these logics, extending the…

In this paper we explain how to attach to a family of $p$-adic representations of a product of Galois groups an overconvergent family of multivariable $(\varphi,\Gamma)$-modules, generalizing results from Pal-Zabradi and…

The notion of nearly abelian rational semigroup was introduced by Hinkannen and Martin. In this paper, we have introduced the notion of nearly abelian transcendental semigroup. We have extended the results of nearly abelian rational…

In the first half of this paper, we outline the construction of a new class of abelian pro-$p$ groups, which covers all countably-based pro-$p$ groups. In the second half, we study them, and classify them up to topological isomorphism and…