Related papers: Explicit non-abelian Lubin-Tate theory for GL(2)

In previous work, the authors constructed and studied a lift of the Galois correspondence to stable homotopy categories. In particular, if $L/k$ is a finite Galois extension of fields with Galois group $G$, there is a functor $c_{L/k}^*$…

Let F be a non-archimedean local field with residual characteristic p, and k an algebraically closed field with characteristic l, where l different from p. Let Rep_k(SL_n(F)) be the category of smooth k-representations of SL_n(F). In this…

Let A be the jacobian variety of a hyperelliptic curve defined over a number field k. We provide a decomposition formula for the Faltings height of A and for the N\'eron-Tate height of k-rational points on A. We formulate a question of…

We first study geometrically oriented truncation associated with stability along the line of Arthur's analytic truncation. Then, we give a detailed discussion on the so-called Abelian Parts of non-abelian L functions, using an advanced…

We prove a cohomological formula for non-critical residues of degree eight automorphic $L$-functions of $\mathrm{GSp}(4) \times \mathrm{GL}(2)$ in the spirit of Beilinson conjecture. We rely on the cohomological interpretation of an…

Let $F$ be a non archimedian local field and $H_n(F)$ the Shalika subgroup of $GL_{2n}(F)$. We prove an explicit Plancherel formula for $H_n(F) \backslash GL_{2n}(F)$ using the theory of Jacquet-Shalika of zeta functions and we deduce…

We use relations between the base change representations and theta lifts, to give a new proof to the local period problems of SL(2) over a nonarchimedean quadratic field extension E/F. Then we will verify the Prasad conjecture for SL(2).…

Let $F$ be a non-archimedean local field. Let $\pi_1$ and $\pi_2$ be irreducible Arthur type representations of $\mathrm{GL}_n(F)$ and $\mathrm{GL}_{n-1}(F)$ respectively. We study Ext branching laws when $\pi_1$ and $\pi_2$ are products of…

In this paper, we completely prove a standard conjecture on the local converse theorem for generic representations of GLn(F), where F is a non-archimedean local field.

A non-abelian topological quantum field theory describing the scattering of self-dual field configurations over topologically non-trivial Riemann surfaces, arising from the reduction of 4-dim self-dual Yang-Mills fields, is introduced. It…

All gradings by abelian groups are classified on the following algebras over an algebraically closed field of characteristic not 2: the simple Lie algebra of type $G_2$ (characteristic not 3), the exceptional simple Jordan algebra, and the…

Let F be a number field and N an integral ideal in its ring of integers. Let f be a modular newform over F of level Gamma0(N) with rational Fourier coefficients. Under certain additional conditions, Guitart-Masdeu-Sengun constructed a…

Let p and l be two distinct primes. We show how, under a certain congruence hypothesis, the mod l cohomology of the Lubin-Tate tower together with a certain Lefschetz operator provides a geometric interpretation of Vigneras' Langlands…

Let C/K be a curve over a local field. We study the natural semilinear action of Galois on the minimal regular model of C over a field F where it becomes semistable. This allows us to describe the Galois action on the l-adic Tate module of…

Let $G$ and $\tilde G$ be reductive groups over a local field $F$. Let $\eta : \tilde G \to G$ be a $F$-homomorphism with commutative kernel and commutative cokernel. We investigate the pullbacks of irreducible admissible…

All kinds of global correspondences of Langlands are evaluated from the functional representation spaces of the algebraic bilinear semigroups GL2(.x.) with entries in products,right by left,of sets of archimedean increasing completions.…

Let $L/K$ be a Galois extension of local fields of characteristic $0$ with Galois group $G$. If $\mathcal{F}$ is a formal group over the ring of integers in $K$, one can associate to $\mathcal F$ and each positive integer $n$ a $G$-module…

Let $F$ be a local field of characteristic $p>0$. By adapting methods of Scholze, we give a new proof of the local Langlands correspondence for $\GL_n$ over $F$. More specifically, we construct $\ell$-adic Galois representations associated…

In this article, we give a new method for proving Howe correspondence in the case of dual pairs of type $({\rm GL}_n, {\rm GL}_m)$ over a non-Archimedean locally compact field $F$. The proof consists in combining a study on Kudla's…

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…