Related papers: The semi-stable Local Langlands Correspondence

We discuss pointwise behavior of weak supersolutions for a class of doubly nonlinear parabolic fractional $p$-Laplace equations which includes the fractional parabolic $p$-Laplace equation and the fractional porous medium equation. More…

In 1976, Deligne and Lusztig realized the representation theory of finite groups of Lie type inside \'etale cohomology of certain algebraic varieties. Recently, a $p$-adic version of this theory started to emerge: there are $p$-adic…

Fix a prime $p\geq5$, an integer $N\geq1$ relatively prime to $p$, and an irreducible residual global Galois representation $\bar{r}: Gal_{\mathbb{Q}}\rightarrow GL_2(\mathbb{F}_p)$. In this paper, we utilize ghost series to study $p$-adic…

Inspired by Emerton's work for GL(2), we study the completed cohomology of the tower of finite sets associated with a definite unitary group in two variables. When p splits (and other technical assumptions are fulfilled), we show that the…

Let $F$ be a non-Archimedean local field of residual characteristic $p$, and $\ell$ a prime number, $\ell \neq p$. We consider the Langlands correspondence, between irreducible, $n$-dimensional, smooth representations of the Weil group of…

In this paper we are interested in the geometric local theta correspondence at the Iwahori level for dual reductive pairs $(G,H)$ of type II over a non-Archimedean field of characteristic $p\neq 2$ in the framework of the geometric…

The parabolic algebra A_p is the weakly closed algebra on L^2(R) generated by the unitary semigroup of right translations and the unitary semigroup of multiplication by the analytic exponential functions e^{i\lambda x}, \lambda \geq 0. This…

The notion of a p-adic de Rham representation of the absolute Galois group of a p-adic field was introduced about twenty years ago (see e.g. [Fo93]). Three important results for this theory have been obtained recently: The structure theorem…

We develop a local Lie theory for Lie algebras equipped with a quasi-norm, i.e., complete topological vector spaces satisfying a relaxed triangle inequality $\|x+y\|\le \Ctri(\|x\|+\|y\|)$ with $\Ctri\ge 1$. We prove that the…

We show that the continuous cohomology groups of a $ p $-adic reductive group with coefficients in the locally analytic vectors of an admissible $ \mathbb{Q}_p $-Banach space representation are homeomorphic to those with coefficients in the…

The analytic Langlands correspondence was developed by Etingof, Frenkel and Kazhdan in arXiv:1908.09677, arXiv:2103.01509, arXiv:2106.05243, arXiv:2311.03743. For a curve $X$ and a group $G$ over a local field $F$, in the tamely ramified…

In this paper, we prove the "local epsilon-isomorphism conjecture" of Fukaya and Kato for a particular class of Galois modules obtained by tensoring a Zp-lattice in a crystalline representation of the Galois group of Qp with a…

Let $F$ be a totally real number field, $\wp$ a place of $F$ above $p$. Let $\rho$ be a $2$-dimensional $p$-adic representation of $\mathrm{Gal}(\bar{F}/F)$ which appears in the \'etale cohomology of quaternion Shimura curves (thus $\rho$…

We propose a new moduli-theoretic approach to the $p$-adic Simpson correspondence for a smooth proper rigid space $X$ over $\mathbb C_p$ with coefficients in any rigid analytic group $G$, in terms of a comparison of moduli stacks. For its…

The goal of this paper is to show a (derived) $p$-adic Simpson correspondence for (locally) unipotent coefficients on smooth rigid-analytic varieties. Our results depend on a deformation to $\mathbf{B}_\mathtt{dr}^+/\xi^2$, and not on a…

The construction of the $p$-adic local Langlands correspondence for $\mathrm{GL}_2(\mathbf{Q}_p)$ uses in an essential way Fontaine's theory of cyclotomic $(\varphi,\Gamma)$-modules. Here \emph{cyclotomic} means that $\Gamma =…

If a $p$-adic Galois representation $\rho_{f,\nu}:\Gamma_{\mathbb Q} \to \GL_2(E_{f,\nu})$ attached to some eigenform $f$ is residually reducible it will have 2 non-isomorphic reductions, which have the same semi-simplification. In this…

This paper establishes limit theorems and quantitative statistical stability for a class of piecewise partially hyperbolic maps that are not necessarily continuous nor locally invertible. By employing a flexible functional-analytic…

In this paper, we consider the Q-tensor model of nematic liquid crystals, which couples the Navier-Stokes equations with a parabolic-type equation describing the evolution of the directions of the anisotropic molecules, in the half-space.…

In this brief essay a construction of the $2$-variable L-function of Langlands is sketched in terms of monomial resolutions of admissible representations of reductive locally $p$-adic Lie groups.