On the p-Adic Birch, Swinnerton–Dyer Conjecture for Non-semistable Reduction Original Research Article

In this paper, we examine the Iwasawa theory of elliptic cuves E with additive reduction at an odd prime p. By extending Perrin-Riouʹs theory to certain non-semistable representations, we are able to convert Katoʹs zeta-elements into p-adic L-functions. This allows us to deduce the cotorsion of the Selmer group over the cyclotomic imagep-extension of image, and thus prove an inequality in the p-adic Birch and Swinnerton-Dyer Conjecture at primes p whose square divides the conductor of E.