Equivariant Iwasawa theory for elliptic curves

Abstract

We discuss abelian equivariant Iwasawa theory for elliptic curves over Q at good supersingular primes and non-anomalous good ordinary primes. Using Kobayashi's method, we construct equivariant Coleman maps, which send the Beilinson-Kato element to the equivariant p-adic L-functions. Then we propose equivariant main conjectures and, under certain assumptions, prove one divisibility via Euler system machinery. As an application, we prove a case of a conjecture of Mazur-Tate.2010 Mathematics Subject Classification. 11R23.