4 problems

Let $H/F$ be a finite abelian CM extension of a totally real number field $F$, let $S$ contain $S_p(F)$, and let $p>2$. Write $\mathcal O_{H,S}$ for the ring of $S$-integers,…

Let $K/k$ be a Galois extension of number fields with Galois group $G$, let $p$ be an odd prime, let $n>1$, and let $S$ and $T$ be finite non-empty disjoint sets of places of $k$,…

Let $K/k$ be a Galois extension of number fields, with the relevant higher étale cohomology groups and equivariant $L$-values defined as in the paper. The strong Brumer-Stark prope…

Coates–Sinnott conjecture. With this notation, for every prime $\ell\ne p$ and every $n\in\mathbb Z_{\ge 2}$,