16 problems

Let $Y(U^p,\overline{\rho})$ be the eigenvariety locus considered in the paper, with points $x=(\rho,\underline{\delta})$ consisting of a Galois representation and a locally…

Let $x=(\rho,\underline{\delta})\in Y(U^p,\overline{\rho})$ be a crystalline generic strictly dominant point. For each $v\mid p$, let…

Let $\pi$ be symplectic, let $P$ be a spin parabolic, and let $\tilde\pi^P$ be a $P$-refinement. Let $\chi$ be finite order of conductor $p^\beta>1$, and suppose…

Let $\tilde\pi$ be an Iwahori $p$-refinement of a RASCAR of $\mathrm{GL}_4$. The refinement may be optimally $B$-spin, $Q$-spin, or $G$-spin, where $B$, $Q$, and $G$ are respective…

Let $G$ be the reductive group considered in the paper, let $K=K^p\mathrm{Iw}$ be Iwahori level at $p$, and let $\sE_K^G$ be its eigenvariety. Let $x\in\sE_K^G$ be a non-critical c…

Let $G$ be either $\mathrm{GL}_3$ or $\operatorname{Res}_{F/\mathbb{Q}}\mathrm{GL}_2$, where $F$ is an imaginary quadratic field, and let $\alpha$ be a refinement. A refinement var…

For a spherical cuspidal representation of $\mathrm{GL}_4$ with its $p$-refinements, a symplectic family is understood modulo one-dimensional trivial variation. Symplectic-family d…

Let $\mathcal{R}_h$ be the simplicial deformation ring attached to the Hida family. Galatius–Venkatesh vanishing conjecture. One should have … so the induced map $\pi_{\mathbf I}$…

Let $\Lambda$ be the Hida–Iwasawa algebra and let $\Sigma_h$ denote the relevant Hida support locus. Hida–Urban's cohomological non-abelian Leopoldt conjecture. … The paper explain…

Let $R_h$ be the universal minimal ordinary deformation ring and let $\Lambda$ be the Hida–Iwasawa algebra. Deformation-theoretic non-abelian Leopoldt conjecture. … This is identif…

Let $\Lambda$ be the Hida–Iwasawa algebra, let $R_h$ be the universal minimal ordinary deformation ring, let $\mathcal{R}_h$ be the associated simplicial deformation ring, and for…

Let $\mathbb{H}_h^\bullet=e\mathrm{H}^{\bullet}(Y_1(p^\infty),\mathcal{O})$ be the Hida-theoretic cohomology module, and let $q_s$ be the maximal cohomological degree. Hida's conce…

Let $\Lambda_E$ be the regular local ordinary weight algebra of dimension $r=\operatorname{rk}\mathrm T$, let $F_{\mathfrak m}^{\bullet}$ be the complex interpolating the localized…

For $p=2$ and $N=7$, let $\alpha_{\mathcal{L}}^\pm(k,2,7)$ denote the multisets of slopes on the $\pm1$ Atkin–Lehner eigenspaces, let $\alpha_{\mathcal{L}}(k,2,7)$ be their combine…

Let $\mathcal{R}$ be a refinement, let $\lambda$ be the algebraic weight appearing in the associated locally analytic representation, and let $w_0$ be the longest Weyl-group elemen…

Fix distinct primes $p$ and $l$, and an integer $N$ coprime to $pl$. Let $\mathcal{E}$ be the cuspidal eigencurve of tame level $\Gamma_0(Nl)$, parametrising overconvergent cuspida…