8 problems

Let $K$ be the imaginary quadratic field in the setup, let $\mathcal{N}_{\rm Heeg}$ be the set of admissible squarefree products, and let…

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:

Let $f$, $\mathfrak{p}$, and $K$ be fixed, and for each $S\in\mathcal{P}^{\mathrm{indef}}$ let $\kappa_S^\star$ denote the strict Kolyvagin system attached to…

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…

Perrin-Riou's conjecture. For every finite extension $E$ of $\boldsymbol{\textup{Q}}_p$, every finite-order character $\chi:G_{\boldsymbol{\textup{Q}}}\to E^{\times}$ unramified at…