5 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…

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

Stark's conjecture over $\mathbb{Z}$. There is a unique element

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…

Coates–Sinnott conjecture. One has