Related papers: Epipelagic L-packets and rectifying characters

We study the geometry and cohomology of the (generic fibres) of formal deformation schemes of one-dimensional formal modules of finite height. By the work of Boyer (in mixed characterististic) and Harris and Taylor, the l-adic etale…

We determine the parity of the Langlands parameter of a conjugate self-dual supercuspidal representation of GL(n) over a non-archimedean local field by means of the local Jacquet-Langlands correspondence. It gives a partial generalization…

We re-write the character formul{\ae} of Adler and the second-named author in a form amenable to explicit computations in $p$-adic harmonic analysis, and use them to prove the stability of character sums for a modification of Reeder's…

The p-adic local Langlands correspondence for GL_2(Q_p) is given by an exact functor from unitary Banach representations of GL_2(Q_p) to representations of the absolute Galois group G_{Q_p} of Q_p. We prove, using characteristic 0 methods,…

Let $F$ be a non-archimedean local field and $G={\bf{G}}(F)$ the group of $F$-rational points of a connected reductive $F$-group. Then we have the Langlands classification of complex irreducible admissible representations $\pi$ of $G$ in…

For two distinct primes p and l, we investigate the Z_l-cohomology of the Lubin-Tate towers of a p-adic field. We prove that it realizes some version of Langlands and Jacquet-Langlands correspondences for flat families of irreducible…

We survey results related to our geometrization of a part of the $p$-adic local Langlands correspondence for ${\mathrm{GL}}_2({\mathbf Q}_p)$.

We consider the group $SL_2(K)$, where $K$ is a local non-archimedean field of characteristic two. We prove that the depth of any irreducible representation of $SL_2 (K)$ is larger than the depth of the corresponding Langlands parameter,…

We prove a descent criterion for certain families of smooth representations of GL_n(F) (F a p-adic field) in terms of the gamma factors of pairs constructed in previous work of the second author. We then use this descent criterion, together…

On the background of Zhang's local Gross-Zagier formulae for GL(2), we study some p-adic problems. The local Gross-Zagier formulae give identities of very special local geometric data (local linking numbers) with certain local Fourier…

We establish the Geometric Langlands correspondence for rank one groups over the projective line with three points of tame ramification.

This is an exposition of our joint work with Kakde, Silliman, and Wang, in which we prove a version of Ribet's Lemma for $\mathrm{GL}_2$ in the residually indistinguishable case. We suppose we are given a Galois representation taking values…

Using a level-raising argument (and a result of Larsen on the image of Galois representations in compatible systems), we prove that for any automorphic representation $\pi$ for $\U(3)$, the $l$-adic Galois representation $\rho_l$ which is…

The (reduced) characteristic group of a locally conformally product manifold is obtained by restricting the action of its fundamental group to the non-flat factor of the universal cover, and taking the connected component of the identity in…

Let $\mathbf{G}$ be an unramified quasi-split unitary group over a p-adic field of odd residual characteristic. The goal of this paper is to describe the supercuspidal representations within certain L-packets of $\mathbf{G}$, which are…

Let $F/\mathbb{Q}_p$ be finite and let $\mathfrak{X}_G$ be the moduli space of Langlands parameters valued in $G$, in characteristic distinct from $p$. First, we determine the irreducible components of $\mathfrak{X}_G$. Then, we determine…

Let K be a non-archimedean local field and let G be a connected reductive K-group which splits over an unramified extension of K. We investigate supercuspidal unipotent representations of the group G(K). We establish a bijection between the…

The formal degree of a unipotent discrete series character of a simple linear algebraic group over a non-archimedean local field (in the sense of Lusztig), is a rational function of the cardinality q of the residue field. The irreducible…

We prove that the reduction mod \ell of the local Langlands correspondence between supercuspidal representations of GL_n(F), where F is a finite extension of Q_p, and representations of the Galois group of F is well-defined. The results and…

We provide a purely local computation of the (elliptic) twisted (by "transpose-inverse") character of the representation \pi=I(\1) of PGL(3) over a p-adic field induced from the trivial representation of the maximal parabolic subgroup. This…