6 problems

Let $\mathrm{Gamma}$ be the Galois group in the setup, let $U$ be the relevant group of $S$-units, and let $\mathcal{R}_{eta}$ be the regulator map associated with…

Let $H/F$ be a finite abelian CM extension of a totally real number field $F$, let $G={\rm Gal}(H/F)$, let $p>2$ be prime, and let $T$ satisfy ${\rm Hyp}_p^T(H/F)$. Write…

Let $K$ be a totally real number field, let $p$ be an odd prime, and let $L/K$ be a totally real Galois extension that is finite over the cyclotomic $\mathbb{Z}_p$-extension…

Twisted-trace conjecture. The following two assertions hold: 1.…

Stark's conjecture $\mathrm{St}(K/k)$. The conjecture $\mathrm{St}(K/k,S,T,S')$ holds for all choices of $S$, $T$, and $S'$ satisfying these hypotheses. This is the global form of…

Let $L/K$ be a Galois extension of number fields with Galois group $G$, let $r<0$, and let $\mu_{1-r}(L):=(\mathbb{Q}/\mathbb{Z})(1-r)^{G_L}$, where $G_L$ is the absolute Galois gr…