On the Vanishing of Selmer Groups for Elliptic Curves over Ring Class Fields


Let E/Q be an elliptic curve of conductor N without complex multiplication and let K be an imaginary quadratic field of discriminant D prime to N . Assume that the number of primes dividing N and inert in K is odd, and let Hc be the ring class field of K of conductor c prime to ND with Galois group Gc over K. Fix a complex character χ of Gc. Our main result… (More)


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