## Number Theory Seminar: Dragos Ghioca

- Date: 10/06/2011
- Time: 15:00

Simon Fraser University

Title: Roots of unity, torsion on fibers, and preperiodic points for families of rational maps

Abstract:

In

early 1960's, Lang proved that if for a given polynomial G(X,Y) with

complex coefficients, there exist infinitely many pairs (x,y) where both

x and y are roots of unity such that G(x,y) = 0, then essentially

G(X,Y) = X^mY^n - c, for some integers m and n, and a root of unity c.

In 2009, Masser and Zannier proved a result (similar in the spirit of

Lang's result) for torsion points on a family of elliptic curves. In our

talk we explain how both results come from the same general principle

in arithmetic geometry, and at the same time we present a partial result

to a more general conjecturewhich subsumes both Lang and Masser-Zannier

theorems.

For more information please visit Department of Mathematics at SFU