University of Connecticut
Department of Mathematics
Algebra Seminar

Kate Stange
(Brown University)

Elliptic Nets and Elliptic Curves

MSB 118  Tuesday, April 22, 2008 at 3:30 pm




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 higherdimensional analogue over arbitrary fields.
Suppose E is an elliptic curve over a field K, and P_{1}, ..., P_{n} are points on E defined over K. To this information we associate an ndimensional 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 geometric information they contain, including a connection to
generalised Jacobians, the Poincare biextension and the
TateLichtenbaum and Weil pairings on the elliptic curve. 


