Diophantine equations associated to modular curves of small level
by
Imin Chen
Simon Fraser University

Several classes of Fermat type diophantine equations have been successfully resolved using the method of galois representations and modularity. In each case, it is possible to view solutions to the diophantine equation in question as corresponding to certain integral points on modular curves of small level. For instance, if r = 2 and 3, primitive solutions to the equation x^p + y^p = z^r correspond to certain integral points on the modular curve X_0(r). This extra level structure often ends up being the crucial ingredient in eliminating modular forms in the final step of the method. In this talk, we will discuss some further examples of diophantine equations associated to modular curves of small level from the point of view of this method.

Date received: April 27, 2004