Marco Streng (Leiden): Divisibility Sequences for Elliptic Curves with Complex Multiplication

Elliptic divisibility sequences arise as sequences of denominators of the integer multiples of a rational point on an elliptic curve. Such sequences are known to have primitive divisors from some point on. If the elliptic curve has complex multiplication, then we show how the endomorphism ring can be used to index a similar sequence and we prove that this sequence also has primitive divisors. The classical proof fails in this context and will be replaced by an inclusion-exclusion argument and sharper diophantine estimates.