ﻻ يوجد ملخص باللغة العربية
We prove automorphy lifting results for certain essentially conjugate self-dual $p$-adic Galois representations $rho$ over CM imaginary fields $F$, which satisfy in particular that $p$ splits in $F$, and that the restriction of $rho$ on any decomposition group above $p$ is reducible with all the Jordan-Holder factors of dimension at most $2$. We also show some results on Breuils locally analytic socle conjecture in certain non-trianguline case. The main results are obtained by establishing an $R=mathbb{T}$-type result over the $mathrm{GL}_2(mathbb{Q}_p)$-ordinary families considered by Breuil-Ding.
We study some closed rigid subspaces of the eigenvarieties, constructed by using the Jacquet-Emerton functor for parabolic non-Borel subgroups. As an application (and motivation), we prove some new results on Breuils locally analytic socle conjecture for $mathrm{GL}_n(mathbb{Q}_p)$.
Let $rho_p$ be a $3$-dimensional $p$-adic semi-stable representation of $mathrm{Gal}(overline{mathbb{Q}_p}/mathbb{Q}_p)$ with Hodge-Tate weights $(0,1,2)$ (up to shift) and such that $N^2 e 0$ on $D_{mathrm{st}}(rho_p)$. When $rho_p$ comes from an au
In this paper we establish a new case of Langlands functoriality. More precisely, we prove that the tensor product of the compatible system of Galois representations attached to a level-1 classical modular form and the compatible system attached to a
Let $p>2$ be a prime number, and $L$ be a finite extension of $mathbb{Q}_p$, we prove Breuils locally analytic socle conjecture for $mathrm{GL}_2(L)$, showing the existence of all the companion points on the definite (patched) eigenvariety. This work
By work of Belyi, the absolute Galois group $G_{mathbb{Q}}=mathrm{Gal}(overline{mathbb{Q}}/mathbb{Q})$ of the field $mathbb{Q}$ of rational numbers can be embedded into $A=mathrm{Aut}(widehat{F_2})$, the automorphism group of the free profinite group