We prove new potential modularity theorems for n-dimensional essentially self-dual l-adic
representations of the absolute Galois group of a totally real eld. Most notably, in the …

Patching and the p-adic local Langlands correspondenceT1 Page 1 arXiv:1310.0831v5 [math.NT]
1 Jul 2016 Cambridge Journal of Mathematics Volume 0, Number 0, 1, 2014 Patching and the …

Let F be a totally real field, K/F a totally imaginary quadratic extension, d=[F: Q], c∈ Gal (K/F)
the non-trivial Galois automorphism. Let n be a positive integer and G= Gn be the algebraic …

We prove new automorphy lifting theorems for essentially conjugate self-dual Galois
representations into GLn. Existing theorems require that the residual representation have …

We show that the Euler system associated with Rankin–Selberg convolutions of modular
forms, introduced in our earlier works with Lei and Kings, varies analytically as the modular …

We develop a theory of Selmer groups for analytic families of Galois representations, which
are only assumed “ordinary” on the level of their underlying (φ, Γ)-modules. Our approach …

Let E be a number field, pa prime number, S a finite set of places of E containing the places
above p and∞, GE, S the Galois group of a maximal algebraic extension of E unramified …

In this paper we generalize the work of Harris–Soudry–Taylor and construct the compatible
systems of two-dimensional Galois representations attached to cuspidal automorphic …

We prove a descent criterion for certain families of smooth representations of GL _n (F) GL n
(F)(F ap-adic field) in terms of the γ γ-factors of pairs constructed in Moss (Int Math Res Not …

Berger and Colmez (2008) formulated a theory of families of overconvergent étale (φ, Γ)-
modules associated to families of p-adic Galois representations over p-adic Banach …