We discuss the problem of
finding a p-adic L-function attached to an elliptic curve with complex multiplication
over an imaginary quadratic field K, for the case of a prime where the curve has
supersingular reduction. While the case of primes of ordinary reduction has been
extensively studied and is essentially understood, yielding many deep and interesting
results, basic questions remain unanswered in the case of supersingular reduction. We
will discuss a conjecture, related to another in Rubin, 1987, and some ideas related
to the problem in general. The basic tools originate with the work of J.
Coates and A. Wiles in 1977 and 1978, and are developed in the work of K.
Rubin.
