Related papers: $\mathbf{F}_p$-representations over $p$-fields

Let $p>3$ and $F$ be a non-archimedean local field with residue field a proper finite extension of $\mathbb{F}_p$. We construct smooth absolutely irreducible non-admissible representations of $\mathrm{GL}_2(F)$ defined over the residue…

In this paper we interpret the solutions to a particular Galois embedding problem over an extension K/F whose Galois group is a finite, cyclic p group in terms of certain Galois submodules within the parameterizing space of elementary…

Let $L$ be the function field of a projective space ${\mathbb P}^n_k$ over an algebraically closed field $k$ of characteristic zero, and $H$ be the group of projective transformations. An $H$-sheaf ${\mathcal V}$ on ${\mathbb P}^n_k$ is a…

We are given a finite group $H$, an automorphism $\tau$ of $H$ of order $r$, a Galois extension $L/K$ of fields of characteristic zero with cyclic Galois group $\langle\sigma\rangle$ of order $r$, and an absolutely irreducible…

Let $G$ be a semisimple Lie group. We describe the irreducible representations of $G$ by linear isometries on $L_p$-spaces for $p\in (1,+\infty)$ with $p\neq 2.$ More precisely, we show that, for every such representation $\pi,$ there…

Let $F$ be a non-archimedean local field of odd residue characteristic $p$. Let $G$ be the unramified unitary group $U(2, 1)(E/F)$, and $K$ be a maximal compact open subgroup of $G$. For an $\overline{\mathbf{F}}_p$-smooth representation…

Let F be a number field with adele ring A_F, and \pi an isobaric, algebraic automorphic representation of GL_4(A_F) of a fixed archimedean weight, which is quasi-regular, meaning that at every archimedean place v of F, the 4-dimensional…

We classify the finite-dimensional irreducible linear representations of the Baumslag-Solitar groups BS(p,q) = < a, b | a b^p = b^q a > for relatively prime p and q. The general strategy of the argument is to consider the matrix group given…

Let G = Aut(T) be the automorphism group of a regular tree T. We study continuous irreducible representations of G that preserve a continuous strongly nondegenerate sesquilinear form of finite index on a Hilbert space. These are already…

Let k be an algebraically closed field with characteristic l different from p. We show that the supercuspidal support of irreducible smooth k-representations of Levi subgroups M' of SL_n(F) is unique up to M'-conjugation, where F is either…

Let V be a p-adic representation of the absolute Galois group G of Q_p that becomes crystalline over a finite tame extension, and assume p odd. We provide necessary and sufficient conditions for V to be isomorphic to the Tate module V_p(A)…

Let $F/F_0$ be a quadratic extension of non-Archimedean locally compact fields of residual characteristic $p\neq2$ with Galois automorphism $\sigma$, and let $R$ be an algebraically closed field of characteristic $\ell\notin\{0,p\}$. We…

Let K be a finite extension of Q_p with residue field F_q and let P(T) = T^d + a_{d-1}T^{d-1} + ... +a_1 T, where d is a power of q and a_i is in the maximal ideal of K for all i. Let u_0 be a uniformizer of O_K and let {u_n}_{n \geq 0} be…

For any number field K, it is unknown which finite groups appear as Galois groups of extensions L/K such that L is a maximal subfield of a division algebra with center K (a K-division algebra). For K=Q, the answer is described by the long…

We obtain a complete classification of the continuous unitary representations of oligomorphic permutation groups (those include the infinite permutation group $S_\infty$, the automorphism group of the countable dense linear order, the…

Let $p\geq 5$ be a prime number. In this paper, we construct Galois representations associated with modular forms for which the dimension of the $p$-torsion in the Bloch-Kato Selmer group can be made arbitrarily large. Our result extends…

Let $F$ be a local field over $\mathbf{Q}_p$ or $\mathbf{F}_p((t))$, and let $D$ be a central simple division algebra over $F$ of degree $d$. In the $p$-adic case, we assume $p>de+1$ where $e$ is the ramification degree over $\mathbf{Q}_p$;…

Let $F$ be a $p$-adic field and $\mathbf{U}$ be a unipotent group defined over $F$, and set $U=\mathbf{U}(F)$. Let $\sigma$ be an involution of $\mathbf{U}$ defined over $F$. Adapting the arguments of Yves Benoist in the real case, we prove…

Let $N/K$ be a finite Galois extension of $p$-adic number fields and let $\rho^\mathrm{nr} : G_K \to \mathrm{Gl}_r(\mathbb Z_p)$ be an $r$-dimensional unramified representation of the absolute Galois group $G_K$ which is the restriction of…

Let $F$ be a non-archimedean local field of characteristic different from 2 and residual characteristic $p$. This paper concerns the $\ell$-modular representations of a connected reductive group $G$ distinguished by a Galois involution,…