Anticyclotomic p-ordinary Iwasawa Theory of Elliptic Modular Forms

Abstract

This is the first in a series of articles where we will study the Iwasawa theory of an elliptic modular form f along the anticyclotomic Zp-tower of an imaginary quadratic field K where the prime p splits completely. Our goal in this portion is to prove the Iwasawa main conjecture for suitable twists of f assuming that f is p-ordinary, both in the definite and indefinite setups simultaneously, via an analysis of Beilinson-Flach elements.

Some corrections on CM Hida families in Section 3

References in corpus (6)

• Rankin--Eisenstein classes and explicit reciprocity laws
• Rankin--Eisenstein classes for modular forms
• Heegner Point Kolyvagin System and Iwasawa Main Conjecture
• Rankin-Selberg Euler systems and p-adic interpolation
• Iwasawa Main Conjecture for Rankin-Selberg $p$-adic $L$-functions: Non-Ordinary Case
• $p$-adic heights of Heegner points and Beilinson-Flach elements

Cited by in corpus (2)

• $p$-adic heights of Heegner points and Beilinson-Flach elements
• Beilinson-Kato and Beilinson-Flach elements, Coleman-Rubin-Stark classes, Heegner points and the Perrin-Riou Conjecture