The anticyclotomic Main Conjecture for elliptic curves at supersingular primes

The Main Conjecture of Iwasawa theory for an elliptic curve E over Q and the anticyclotomic Z(p)-extension of an imaginary quadratic field K was studied in [2], in the case where p is a prime of ordinary reduction for E. Analogous results are formulated, and proved, in the case where p is a prime of supersingular reduction. The foundational study of supersingular main conjectures carried out by Perrin-Riou, Pollack, Kurihara, Kobayashi and Iovita and Pollack are required to handle this case in which many of the simplifying features of the ordinary setting break down.