title: On the p-adic Birch, Swinnerton-Dyer Conjecture for non-semistable reduction
abstract: In this paper, we examine the Iwasawa theory of elliptic curves E with additive reduction at an odd prime p. By extending Perrin-Riou's theory to certain nonsemistable 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/sub 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
keyphrases: p-adic Birch Swinnerton-Dyer conjecture elliptic curves additive reduction Perrin-Riou's theory p-adic L-functions cotorsion Selmer group cyclotomic Z/sub p/-extension nonsemistable reduction lwasawa theory