  We reveal a new and refined application of (a weaker statement than) the
Iwasawa main conjecture for elliptic curves to the structure of Selmer groups
of elliptic curves of arbitrary rank. For a large class of elliptic curves, we
obtain the following arithmetic consequences.
  1. Kato's Kolyvagin systems is non-trivial. It is the cyclotomic analogue of
the Kolyvagin conjecture.
  2. The structure of Selmer groups of elliptic curves over the rationals is
completely determined in terms of certain modular symbols. It is a structural
refinement of Birch and Swinnerton-Dyer conjecture.
  3. The rank zero $p$-converse, the $p$-parity conjecture, and a new upper
bound of the ranks of elliptic curves are obtained.
  4. The conjecture of Kurihara on the semi-local description of mod $p$ Selmer
groups is confirmed.
  5. An application of the $p$-adic Birch and Swinnerton-Dyer conjecture to the
structure of Iwasawa modules is discussed.
