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 mu-invariants of several anticyclotomic Selmer groups.

Automated summary

Under certain hypotheses, we improve upon Kobayahsi-Ota's result and show that the same inclusion holds integrally for the Iwasawa main conjecture of f. Our result implies the vanishing of the Iwasawa mu-invariants of several anticyclotomic Selmer groups.