4 problems

Fix a prime $q\neq p$ splitting in $E$, choose $q'$ as in the source, and let $G$ be a unitary group in $d$ variables attached to $E/\mathbb{Q}$ satisfying the stated conditions at…

Let $L$ be a finite extension of ${\mathbb Q}_p$, let $\mathscr{S}_{\mathrm{irr}}$ parameterize the two-dimensional irreducible trianguline representations, and for…

Let $\mathscr{E}^0$ be the semistable, distinct-eigenvalue locus of the eigencurve, let $\mathscr{V}^0$ be its rank-$2$ family of Galois representations, and set … For each…

Let $\mathscr{X}/E$ be a reduced, separated rigid analytic space, and let $\mathscr{D}$ be a locally free sheaf of $(\varphi,\Gamma_K)$-modules over…