Abstract: I will discuss recent work with Ted Chinburg, supported by a NARC grant this summer. I will start by defining the equivariant Riemann-Roch formula for an algebraic curve with a finite group action, and the ramification module that appears in that formula. The ramification module is a representation of the finite group; in previous work with David Joyner we gave a simple formula for this representation if it can be defined over the rational numbers. The rationality question turns out to be an interesting question about the rationality of certain sums of roots of unity, which I will answer.