Boston University Algebra Seminar

Boston University Algebra Seminar -- Spring 2007

Elliptic Nets

Katherine Stange
(Brown University and Microsoft Research)

Monday, Novemeber 5th at 4:15pm
111 Cummington Street, MCS 135


Elliptic divisibility sequences are integer recurrence sequences, each of which is associated to an elliptic curve over the rationals together with a rational point on that curve. I'll give the background on these and present a higher-dimensional analogue over arbitrary base fields. Suppose E is an elliptic curve over a field K, and P1, ..., Pn are points on E defined over K. To this information we associate an n-dimensional array of values of K satisfying a complicated nonlinear recurrence relation. These are called elliptic nets. All elliptic nets arise from elliptic curves in this manner. I'll explore some of the properties of elliptic nets and the information they contain.