On the BDP Iwasawa main conjecture for modular forms.

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