Iwasawa Main Conjecture for Rankin-Selberg $p$-adic $L$-functions: Non-Ordinary Case

Abstract

In this paper we prove that the $p$-adic $L$-function that interpolates the Rankin-Selberg product of a general weight two modular form which is unramified and non-ordinary at $p$, and an ordinary CM form of higher weight contains the characteristic ideal of the corresponding Selmer group. This is one divisibility of the Iwasawa-Greenberg main conjecture for the $p$-adic $L$-function. This generalizes an earlier work of the author to the non-ordinary case. The result of this paper plays a crucial role in the proof of Iwasawa main conjecture and refined Birch-Swinnerton-Dyer formula for supersingular elliptic curves.

It is completely re-written by the author with Francesc Castella and Zheng Liu as a collaboration, as arXiv:2109.08375

References in corpus (3)

• Heegner Point Kolyvagin System and Iwasawa Main Conjecture
• A proof of the Howe duality conjecture
• Iwasawa Main Conjecture for Heegner Points: Supersingular Case

Cited by in corpus (2)

• Iwasawa Main Conjecture for Supersingular Elliptic Curves and BSD conjecture
• Anticyclotomic p-ordinary Iwasawa Theory of Elliptic Modular Forms