On pairings in elliptic curves over global fields

In this paper the author constructs and investigates the nondegeneracy of pairings in the Galois cohomology of objects naturally attached to an elliptic curve defined over a global field. He constructs a series of curves over a global function field that have finite $\text{ш}$ and among whose minimal models are surfaces of arbitrarily large arithmetic genus.
Bibliography: 49 titles.