Related papers: Simple $\mathcal{L}$-invariants for $\mathrm{GL}_n…

Let F be a finite extension of Q_p. Using the mod p Satake transform, we define what it means for an irreducible admissible smooth representation of an F-split p-adic reductive group over \bar F_p to be supersingular. We then give the…

We prove a conjecture of Colmez concerning the reduction modulo $p$ of invariant lattices in irreducible admissible unitary $p$-adic Banach space representations of $GL_2(Q_p)$ with $p\ge 5$. This enables us to restate nicely the $p$-adic…

Half-integral weight modular forms are naturally viewed as automorphic forms on the so-called metaplectic covering of $\operatorname{GL}_2(\mathbf{A}_{\mathbf{Q}})$ -- a central extension by the roots of unity $\mu_2$ in $\mathbf{Q}$. For…

Let $A_g$ be an abelian variety of dimension $g$ and $p$-rank $\lambda \leq 1$ over an algebraically closed field of characteristic $p>0$. We compute the number of homomorphisms from $\pi_1^{\text{\'et}}(A_g,a)$ to $GL_n(\mathbb F_q)$,…

Let $G$ be a $p$-divisible group over a complete discrete valuation ring $R$ of characteristic $p$. The generic fiber of $G$ determines a Galois representation $\rho$. The image of $\rho$ admits a ramification filtration and a Lie…

Let $G_n=\operatorname{GL}_n(F)$, where $F$ is a non-archimedean local field with residue characteristic $p$. Our starting point is the Bernstein-decomposition of the representation category of $G_n$ over an algebraically closed field of…

We compute the arithmetic L-invariants (of Greenberg-Benois) of twists of symmetric powers of p-adic Galois representations attached to Iwahori level Hilbert modular forms (under some technical conditions). Our method uses the automorphy of…

The l-adic parabolic cohomology groups attached to noncongruence subgroups of SL_2(Z) are finite-dimensional representations of Gal(Qbar/F) for some number field F. We exhibit examples (with F=Q) giving rise to Galois representations whose…

Let $K/F$ be a quadratic extension of $p$-adic fields, $\sigma$ the nontrivial element of the Galois group of $K$ over $F$, and $\pi$ a quasi-square-integrable representation of $GL(n,K)$. Denoting by $\pi^{\vee}$ the smooth contragredient…

Let $(G,\theta)$ be a Banach--Lie group with involutive automorphism $\theta$, $\g = \fh \oplus \fq$ be the $\theta$-eigenspaces in the Lie algebra $\g$ of $G$, and $H = (G^\theta)_0$ be the identity component of its group of fixed points.…

We prove a new upper bound for the dimension of the space of cohomological automorphic forms of fixed level and growing parallel weight on $\mathrm{GL}_2$ over a number field which is not totally real, improving the one obtained by…

For a $p$-adic field $F$, the space of pro-$p$-Iwahori invariants of a universal supersingular mod $p$ representation $\tau$ of ${\rm GL}_2(F)$ is determined in the works of Breuil, Schein, and Hendel. The representation $\tau$ is…

In this paper, we study Fontaine-Laffaille, self-dual deformations of a mod p non-semisimple Galois representation of dimension n with its Jordan-Holder factors being three mutually non-isomorphic absolutely irreducible representations. We…

For each subgroup of GL_2(F_p) or order divisible by p, generated by (pseudo-)reflections, we compute the ideals of stable and generalized invariants. These groups and these ideals are related to the cohomology of compact Lie groups,…

In this paper we study the images of certain families $\{\rho_{\pi,\ell} \}_\ell$ of $G_2$-valued Galois representations of $\mbox{Gal}(\overline{F}/F)$ associated to $L$-algebraic regular, self-dual, cuspidal automorphic representations…

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…

We compute the universal deformations of cuspidal representations $\pi$ of $\GL_2(F)$ over an algebraically closed field of characteristic $l$, where $F$ is a local field of residue characteristic $p$ not equal to $l$. When $\pi$ is…

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…

We present a collection of conjectural trace identities and explain why they are equivalent to base change and descent of automorphic representations of $\mathrm{GL}_n(\mathbb{A}_F)$ along nonsolvable extensions (under some simplifying…

In this paper, we explicitly determine the local $2$-adic component of a non-selfdual automorphic representation $\Pi$ of $\mathrm{GL}_3$ constructed by van Geemen and Top. We prove that $\Pi_2$ is a parabolically induced representation of…