Related papers: Patching and the p-adic Langlands program for GL(2…

We give a proof of the Breuil-Schneider conjecture in a large number of cases, which complement the indecomposable case, which we dealt with earlier in [Sor]. In some sense, only the Steinberg representation lies at the intersection of the…

This is the sequel to arXiv:2007.01364v1. Let $F$ be any local field with residue characteristic $p>0$, and $\mathcal{H}^{(1)}_{\overline{\mathbb{F}}_p}$ be the mod $p$ pro-$p$-Iwahori Hecke algebra of $\mathbf{GL_2}(F)$. In…

We show that the conjectural mod $p$ local Langlands correspondence can be realised in the mod $p$ cohomology of the Lubin-Tate towers. The proof utilizes a well known conjecture of Buzzard-Diamond-Jarvis \cite[Conj. 4.9]{BDJ10}, a study of…

We analyse the mod p \'etale cohomology of the Lubin-Tate tower both with compact support and without support. We prove that there are no supersingular representations in the H^1_c of the Lubin-Tate tower. On the other hand, we show that in…

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…

We develop further the Lenard-Magri scheme of integrability for a pair of compatible non-local Poisson structures, which we discussed in Part I. We apply this scheme to several such pairs, proving thereby integrability of various evolution…

The paper revisits concretely the algebraic K-theory in the light of the global program of Langlands by taking into account the new algebraic interpretation of homotopy viewed as deformation(s) of Galois representations given by…

This is the final version, to appear in Commentarii Mathematici Helvetici.

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.

We prove the existence of a new structure on the first Galois cohomology of generic families of symplectic self-dual $p$-adic representations of $G_{\mathbb{Q}_p}$ of rank two (a local sign decomposition): a functorial decomposition into…

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 study the variation of the local Langlands correspondence for ${\rm GL}_{n}$ in characteristic-zero families. We establish an existence and uniqueness theorem for a correspondence in families, as well as a recognition theorem for when a…

We use the Taylor-Wiles-Kisin patching method to investigate the multiplicities with which Galois representations occur in the mod $\ell$ cohomology of Shimura curves over totally real number fields. Our method relies on explicit…

In the case of split $GSpin$ groups, we prove an equality of $L$-functions between automorphic local $L$-functions defined by the Langlands-Shahidi method and local Artin $L$-functions. Our method of proof is based on previous results of…

We introduce an analog of part of the Langlands-Shahidi method to the p-adic setting, constructing reciprocals of certain p-adic L-functions using the nonconstant terms of the Fourier expansions of Eisenstein series. We carry out the method…

In this paper, we give a purely geometric approach to the local Jacquet-Langlands correspondence for GL(n) over a p-adic field, under the assumption that the invariant of the division algebra is 1/n. We use the l-adic etale cohomology of…

We give a direct approach to recover some of the results of Wiles and Tayor on modularity of certain 2-dimensional p-adic representations of the absolute Galois group of Q.

This sequel to Derived Langlands II studies some PSH algebras and their numerical invariants, which generalise the epsilon factors of the local Langlands Programme. It also describes a conjectural Hopf algebra structure on the sum of the…

We describe the de Rham complex of the \'etale coverings of Drinfeld's p-adic upper half-plane for GL_2(Q_p). Conjectured by Breuil and Strauch, this description gives a geometric realization of the p-adic local Langlands correspondence for…

We continue to develop the analytic Langlands program for curves over local fields initiated in arXiv:1908.09677, arXiv:2103.01509 following a suggestion of Langlands and a work of Teschner. Namely, we study the Hecke operators introduced…