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 ℤ p {\mathbb{Z}_{p}} -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.