Mathematical Research Letters
Volume 14 (2007)
A generalization of the Cassels-Tate dual exact sequence
Pages: 295 – 302
We extend the first part of the well-known Cassels-Tate dual exact sequence for abelian varieties $A$ over global fields $K$ in two directions: we treat the $p$-primary component in the function field case, where $p$ is the characteristic of $K$, and we dispense with the assumption that the Tate-Shafarevich group of $A$ is finite.