3 problems

Let $A$ be an abelian variety, let $F/k$ be a finite Galois extension with group $G$, let $S$ be the specified finite set of places, and let $\widehat G$ be the set of irreducible…

Let $F/E$ be a Galois extension with Galois group $\Gamma$, and let $T\Omega^\mathrm{loc}(F/E,1)$ be the locally defined element of $K_0(\mathbb Z[\Gamma],\mathbb R)$. Global equiva…

Let $L/\mathbb{Q}_p$ be the extension, let $T$ be the $p$-adic Tate module of the formal group $\mathcal{F}$, and let $\tilde{y}$ be the component of the equivariant epsilon isomor…