7 problems

Let $K$ be the imaginary quadratic field in the setup, let $\boldsymbol{\kappa}^{\rm Heeg}$ be the Heegner-point Kolyvagin system, and let…

Strict Kolyvagin conjecture. The strict Kolyvagin set is nontrivial:

Kolyvagin's conjecture. The set of Kolyvagin classes is nontrivial:

Let $\kappa^{\mathrm{st}}_{f,\infty}$ be the strict Kolyvagin set consisting of the classes $c_1(f,n)$ as $n$ ranges over the Kolyvagin indices. Strong Kolyvagin conjecture. … This…

Let $T$ be the $p$-adic Galois representation and let $\mathfrak{K}(T)$ be the $\Lambda$-module of Kolyvagin determinants. For an even Dirichlet character $\theta$ and…

Let $K$ be the relevant number field, let $K_p$ denote its $p$-adic localization, let $\mathbb{T}$ be the associated big representation, and let $r_{\mathrm{an}}(\mathscr{M})$ be t…

Suppose $F$ is a real quadratic field and $K_n=F(\boldsymbol{\mu}_n)$, where $n$ is prime to the conductor of $F/\mathbf{Q}$. Let…