Graduate School of Mathematics and Applications
Simon Fraser University, Vancouver, Canada
As a program under the Graduate School of Mathematics and Applications ('Forskerskolen for Matematik og Anvendelser'), Imin Chen, Simon Fraser University, Vancouver, Canada, will give a mini-course with the title:
Introduction to Q-curves
The lectures take place on the following dates:
Monday, 24 November, 2008, 15.15 - 17.00 in Aud. 8,
Thursday, 27 November, 2008, 13.15 - 14.00 in Aud. 9.
Abstract: A Q-curve is an elliptic curve C defined over a number field K such that each of its conjugates over Q are isogenous to C. There are Galois representations of G_K on the Tate modules of C, but because the isogeny class of C is defined over Q, one can in fact attach Galois representations of G_Q to C, and also make sense of modularity of C using classical modular forms with character.
In these lectures, I will review some basic background regarding Q-curves and illustrate by explicit examples the process by which one attaches Galois representations of G_Q to a Q-curve C. If time permits, some diophantine applications will also be described.