5 problems

Let $\mathbb{T}^S(K^p,\mathcal{O})_{\mathfrak{m}}$ be the localized Hecke algebra, let $\varphi:\mathbb{T}^S(K^p,\mathcal{O})_{\mathfrak{m}}\to\mathcal{O}$ be an eigensystem, and l…

Let $G$ be the group in the source, let $\mu$ be the specified minuscule cocharacter, let $GDR^{\Psi-\mathrm{la}}_{\lambda}$ be the geometric locally analytic de Rham complex of we…

Let $G_{\mathbb{Q}_p}:=\operatorname{Res}_{F_w/\mathbb{Q}_p}\mathrm{GL}_{2,F_w}$, let $\mu$ be the specified minuscule cocharacter, and let $\mathscr{F}\!\ell^b$ be the Newton stra…

Let $\mathscr{F}\!\ell$ be the flag variety, let $GDR^{\mathrm{la}}_0$ be the geometric locally analytic de Rham complex, let $d$ be the relevant cohomological degree, and let…

Let $\mathscr{F}\!\ell$ be the flag variety, let $N_0$ be the Fontaine operator, let $d$ be the relevant cohomological degree, and let $\mathfrak{m}$ be the specified Hecke ideal.…