Lectures on the Iwasawa Theory of Elliptic Curves

Recent Results in the GL2 Iwasawa Theory of Elliptic Curves without Complex Multiplication

Recently new results have been obtained in the GL2 Iwasawa theory of elliptic curves without complex multiplication. This article is a survey of some of those results. Mathematics Subject Classification: 11G05, 11R23

Anticyclotomic Iwasawa Theory of Cm Elliptic Curves Ii Adebisi Agboola and Benjamin Howard

We study the Iwasawa theory of a CM elliptic curve E in the anticyclotomic Zpextension D∞ of the CM field K, where p is a prime of good, supersingular reduction for E. Our main result yields an asymptotic formula for the corank of the p-primary Selmer group of E along the extension D∞/K.

Elliptic Curves with Complex Multiplication and the Conjecture of Birch and Swinnerton-Dyer

1. Quick Review of Elliptic Curves 2 2. Elliptic Curves over C 4 3. Elliptic Curves over Local Fields 6 4. Elliptic Curves over Number Fields 12 5. Elliptic Curves with Complex Multiplication 15 6. Descent 22 7. Elliptic Units 27 8. Euler Systems 37 9. Bounding Ideal Class Groups 43 10. The Theorem of Coates and Wiles 47 11. Iwasawa Theory and the “Main Conjecture” 50 12. Computing the Selmer G...

Anticyclotomic Iwasawa Theory of Cm Elliptic Curves Ii

We study the Iwasawa theory of a CM elliptic curve E in the anticyclotomic Zpextension D∞ of the CM field K, where p is a prime of good, supersingular reduction for E. Our main result yields an asymptotic formula for the corank of the p-primary Selmer group of E along the extension D∞/K.

Iwasawa Theory of Elliptic Curves with Complex Multiplication