On the Iwasawa main conjecture for generalized Heegner classes in a quaternionic setting

We prove one divisibility relation of the anticyclotomic Iwasawa Main Conjecture for a higher weight ordinary modular form f and an imaginary quadratic field satisfying a "relaxed" Heegner hypothesis. Let Lambda be the anticyclotomic Iwasawa algebra. Following the approach of Howard and Longo-Vigni, we construct the Lambda-adic Kolyvagin system of generalized Heegner classes coming from Heegner points on a suitable Shimura curve. As its application, we also prove one divisibility relation in the Iwasawa-Greenberg main conjecture for the p-adic L-function defined by Magrone.