Lubin--Tate Iwasawa Theory for CM elliptic curves with p inert

par Muhammad Manji

jeudi 19 juin 2025, 14:00 → 16:00 Europe/Paris

M7-411

The Iwasawa theory for CM elliptic curves is a rich problem which has been studied over decades. In the 1990s Rubin proved a 2-variable main conjecture without p-adic L-functions independent of splitting behaviour of p, leading to a main conjecture with p-adic L-functions when p splits. However, a 2-variable main conjecture for p inert remains out of reach. In this work, joint with A.Lei, we prove a main conjecture in the Lubin--Tate direction (utilising the full Z_p^2 extension of the CM field). We also extend the interpolation region of the attached p-adic L-function of Schneider-Teitelbaum and demonstrate the relationship between the p-adic periods involved.