3 problems

Let $R^{\operatorname{ps}}_p$ be the relevant pseudodeformation ring, let $E_{\mathfrak{B}}$ be the corresponding Hecke-module coefficient algebra, and let…

Let $U^p$ be a compact open subgroup away from $p$, let $\mathcal{O}$ be the coefficient ring, let $\mathbb{T}^S(U^p)$ be the Hecke algebra, and let $q_0$ be the distinguished homo…

Patched module conjecture. For some integer $m\geq1$, there is an isomorphism of $\overline{R}_\infty[G]$-modules