5 problems

Let $K$ be an imaginary quadratic field, let $D_\infty/K$ be the relevant $\mathbb Z_p^2$-extension, and let $W$ be the associated $p$-adic representation. Write…

Soulé's finiteness conjecture. The group $H^2_p$ is always finite.

Kato's weak Tamagawa number conjecture. There is a subspace $H^{\operatorname{constr}}_{{\cal M}}$ such that $r_{{\cal D}}$ and $r_p$ restricted to it are isomorphisms and $H^2_p$…

Let $I$ be the index set of multi-indices used to define the characters $kappa_{\boldsymbol{m}}$, let $g$ be the associated graded Lie algebra, and let $chi^{\boldsymbol{m}}$ denot…

Let $\rho_{\ell,i}$ be a weakly compatible system of self-dual $\ell$-adic representations, and suppose that for some $\ell$ and $i$ its semisimplification decomposes as … where…