Visibility

In Section 1.1 we introduce visible cohomology classes, then in Section 1.2 we discuss visible elements of Shafarevich-Tate groups. In Section 1.3, we use restriction of scalars to deduce that every cohomology class is visible somewhere.

For a field $K$ and a smooth commutative $K$-group scheme $G$, we write $H^i(K,G)$ to denote the group cohomology $H^i(\Gal(K_s/K),G(K_s))$ where $K_s$ is a fixed separable closure of $K$; equivalently, $H^i(K,G)$ denotes the $i$th étale cohomology of $G$ viewed as an étale sheaf on $\Spec(K)_{\mbox{\small\rm\'et}}$.