✦ LIBER ✦
On the p-Adic Birch, Swinnerton–Dyer Conjecture for Non-semistable Reduction
✍ Scribed by Daniel Delbourgo
- Publisher
- Elsevier Science
- Year
- 2002
- Tongue
- English
- Weight
- 363 KB
- Volume
- 95
- Category
- Article
- ISSN
- 0022-314X
No coin nor oath required. For personal study only.
✦ Synopsis
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 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 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.