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This is the first in a series of articles where we will study the Iwasawa theory of an elliptic modular form  f  along the anticyclotomicℤ  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.

Anticyclotomic p -ordinary Iwasawa theory of elliptic modular forms