On the p-adic birch, Swinnerton-Dyer conjecture for non-semistable reduction

In this paper, we examine the Iwasawa theory of elliptic cuves E with additive reduction at an odd prime p. By extending Perrin-Riou's theory to certain non-semistable representations, we are able to convert Kato's zeta-elements into p-adic L-functions. This allows us to deduce the cotorsion of the Selmer group over the cyclotomic Z(p)-extension of Q, and thus prove an inequality in the p-adic Birch and Swinnerton-Dyer Conjecture at primes p whose square divides the conductor of E. (C) 2002 Elsevier Science (USA).