Department of Mathematics2024-11-1020180933-774110.1515/forum-2016-01892-s2.0-85039076777http://dx.doi.org/10.1515/forum-2016-0189https://hdl.handle.net/20.500.14288/17061This 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)-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.MathematicsApplied mathematicsJournal Article1435-5337437914900007Q31180