Number Theory Seminar: Dragos Ghioca

  • Date: 10/06/2011
  • Time: 15:00
Dragos Ghioca

Simon Fraser University


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



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

Other Information: 

For more information please visit Department of Mathematics at SFU