On the BDP Iwasawa main conjecture for modular forms

Let K be an imaginary quadratic field where p splits, $$p\ge 5$$ a prime number and f eigen-newform of even weight level $$N>3$$ that is coprime to p. Under the Heegner hypothesis, Kobayashi–Ota showed one inclusion Iwasawa main conjecture involving Bertolini–Darmon–Prasanna p-adic L-function holds after tensoring by $$\mathbb {Q}_p$$ . certain hypotheses, we improve upon Kobayahsi–Ota’s result show same integrally. Our implies vanishing $$\mu $$ -invariants several anticyclotomic Selmer groups.