4 problems

Let $p>3$ be a prime, and let $K$ be an imaginary quadratic field whose class group has $p$-rank two. Set … Choose a basis $x,y$ of $H^1(G,\mathbb{Z}/p\mathbb{Z})$, and let…

Let $p>3$ be a prime, and let $K$ be an imaginary quadratic field whose class group has $p$-rank two. The Zassenhaus type is the pair $(i,j)$ occurring in the Zassenhaus polynomial…

Tower ground state conjecture. The fields with discriminants $d\in\{-225\,299,-343\,380,-423\,476,-486\,264\}$ of type $\mathrm{F}.7$,…

Extremal root path conjecture. The root path $(\pi^{i-1}(G)\to\pi^i(G))_{1\leq i\leq c-2}$ consists of edges of maximal step size, equal to the nuclear rank: for every…