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 higher-dimensional analogue over arbitrary 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 geometric information they contain, including a connection to generalised Jacobians, the Poincare biextension and the Tate-Lichtenbaum and Weil pairings on the elliptic curve.  

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