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Equivariant Iwasawa theory for elliptic curves. (English) Zbl 07373932

Summary: We discuss abelian equivariant Iwasawa theory for elliptic curves over \({\mathbb{Q}}\) 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.

MSC:

11R23 Iwasawa theory
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