Title: Bloch-Kato conjecture for CM modular forms and Rankin-Selberg convolutions

Abstract: Let E/F be an elliptic curve over a number field F with CM by an imaginary quadratic field K, and assume that the extension of F generated by the torsion points of E is abelian over K. In this talk I will outline a proof of the p-part of the Birch-Swinnerton-Dyer formula for E in analytic rank 1 for primes p>3 of ordinary reduction. For F=Q, this was originally proved by Rubin in 1991 as a consequence of his proof of the Iwasawa main conjecture for K. In contrast, our approach for general F is based on the study of an auxiliary Rankin-Selberg convolution, and also extends to CM abelian varieties A/K and higher weight CM modular forms.