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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 $p>2$ 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
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 decomposi
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
Let $L$ be a finite extension of $mathbb{Q}_p$, and $rho_L$ be an $n$-dimensional semi-stable non crystalline $p$-adic representation of $mathrm{Gal}_L$ with full monodromy rank. Via a study of Breuils (simple) $mathcal{L}$-invariants, we attach to $
Let $p$ be a prime number and $K$ a finite extension of $mathbb{Q}_p$. We state conjectures on the smooth representations of $mathrm{GL}_n(K)$ that occur in spaces of mod $p$ automorphic forms (for compact unitary groups). In particular, when $K$ is