Related papers: Dilogarithm and higher $\mathscr{L}$-invariants fo…

Let $K$ be a finite field extension of $Q_p$ and let $G_K$ be its absolute Galois group. We construct the universal family of filtered $(\phi,N)$-modules, or (more generally) the universal family of $(\phi,N)$-modules with a Hodge-Pink…

We construct a derived variant of Emerton's eigenvarieties using the locally analytic representation theory of $p$-adic groups. The main innovations include comparison and exploitation of two homotopy equivalent completed complexes…

Let $p>3$ be a prime number and let $G_{\mathbb{Q}_p}$ be the absolute Galois group of $\mathbb{Q}_p$. In this paper, we find Galois stable lattices in the irreducible $3$-dimensional semi-stable and non-crystalline representations of…

Let $\pi$ be a cuspidal automorphic representation of $GL_n(\mathbb{A}_\mathbb{Q})$ which satisfies certain reasonable assumptions such as integrality of Hecke polynomials, the existence of mod $\ell$ Galois representations attached to…

We study a natural Hodge theoretic generalization of rational (or $\mathbb{Q}$-)homology manifolds through an invariant ${\rm HRH(Z)}$ where $Z$ is a complex algebraic variety. The defining property of this notion encodes the difference…

In this paper, we study locally analytic vectors in the "partially" completed cohomology of Shimura varieties associated with some rank $2$ unitary groups over a totally real field $F^+$ such that $F^+_v = \mathbb{Q}_{p^2}$ for some…

Let $K$ be the function field of a smooth projective geometrically integral curve over a finite extension of $\mathbb{Q}_p$. Following the works of Harari, Scheiderer, Szamuely, Izquierdo, and Tian, we study the local-global and weak…

Let $p$ be a prime number, $K$ a finite unramified extension of $\mathbb{Q}_p$ and $\mathbb{F}$ a finite extension of $\mathbb{F}_p$. For $\overline{\rho}$ any reducible two-dimensional representation of $\operatorname{Gal}(\overline{K}/K)$…

A novel Hopf algebra $ ( {\tilde G}_{r,s} )$, depending on two deformation parameters and five generators, has been constructed. This $ {\tilde G}_{r,s}$ Hopf algebra might be considered as some quantisation of classical $GL(2) \otimes…

With the Poincar\'e group $\mathbf{R}^{3,\,1}\rtimes O(3,\,1)$ as the model of departure, we focus, for $n=p+q$, $p+q\ge 4$, on the affine indefinite orthogonal group $\mathbf{R}^{p,q}\rtimes SO(p,\,q)$. Denote by $\mathfrak{h}_{p,\,q}$ the…

We determine reductions of 2-dimensional, irreducible, semi-stable, and non-crystalline representations of $\mathrm{Gal}(\overline{\mathbb Q}_p/\mathbb Q_p)$ with Hodge--Tate weights $0 < k-1$ and with $\mathcal L$-invariant whose $p$-adic…

Let $G=Sp(4,\mathbb{R})$ and let $\pi$ be an irreducible, unitary representation of $G$ which is cohomological with respect to trivial coefficients. Using the inclusion from $SO(5,\mathbb{C})$ to $GL(5,\mathbb{C})$, we transfer $\pi$ to an…

Under standard assumptions, we compute the GK-dimension of Hecke eigenspaces in the mod $p$ cohomology of an inner form $D^\times$ of $\mathrm{GL}_2$ over a totally real field unramified at $p$, allowing $D$ to be a division algebra at $p$.…

Let $p \geq 5$ be a prime number and let $G = SL_2(\mathbb{Q}_p)$. Let $\Xi$ = Spec$(Z)$ denote the spectrum of the centre $Z$ of the pro-$p$ Iwahori Hecke algebra of $G$ with coefficients in a field $k$ of characteristic $p$. Let…

Let $p$ be a prime number, $K$ a finite unramified extension of $\mathbb{Q}_p$ and $\mathbb{F}$ a finite extension of $\mathbb{F}_p$. Using perfectoid spaces we associate to any finite-dimensional continuous representation $\overline{\rho}$…

For $p\in (1,\infty)$, we study representations of \'etale groupoids on $L^{p}$-spaces. Our main result is a generalization of Renault's disintegration theorem for representations of \'etale groupoids on Hilbert spaces. We establish a…

Let $F$ be a p-adic local field and $G=GL_2(F)$. Let $\mathcal{H}^{(1)}$ be the pro-p Iwahori-Hecke algebra of $G$ with coefficients in an algebraic closure of $\mathbb{F}_p$. We show that the supersingular irreducible…

Given a locally compact quantum group $\mathbb G$, we define and study representations and C$^\ast$-completions of the convolution algebra $L_1(\mathbb G)$ associated with various linear subspaces of the multiplier algebra $C_b(\mathbb G)$.…

Let L be a finite extension of Qp, and let K be a spherically complete non-archimedean extension field of L. In this paper we introduce a restricted category of continuous representations of locally L-analytic groups G in locally convex…

Let $n>1$, $e\geq 0$ and a prime number $p\geq 2^{n+2+2e}+3$, such that the index of regularity of $p$ is $\leq e$. We show that there are infinitely many irreducible Galois representations $\rho: Gal(\bar{\mathbb{Q}}/\mathbb{Q})\rightarrow…