Weil-Châtelet group (reviewed)

The Weil-Châtelet group Ш of an abelian variety $A$ over a field $K$ is the group of principal homogenous spaces of $A$.

It can also be defined as the Galois cohomology group $H^1(G_K,A)$, where $G_K$ is the absolute Galois group of $K$.