On the Shafarevich–Tate group of an elliptic curve

The paper deals with the group of locally trivial principal homogeneous spaces over an elliptic curve. Duality is proven between the group of those spaces having a point of finite order locally with the exception of prime divisors, and the factor group of those of them which are infinitely divisible in the group of principal homogeneous spaces having a local rational point with respect to all divisors besides the singular ones.