3 problems

Mazur--Tate's refined exceptional zero conjecture. One has

The twisted exceptional zero conjecture. For every such $\chi$,

Let $\Lambda=\mathcal{O}_p[[\Gamma]]$, let $(U_\infty')^\chi$ be the $\chi$-component of the inverse limit of the $p$-unit modules, let $\varepsilon_\infty^\chi$ be the inverse-lim…