Number Theory Seminar

Patrick Meisner, Concordia University

“Distribution of the Number of Points on Curves over Fq”

Classical results due to Katz and Sarnak show that the number of points on curves in families over Fq is distributed as the trace of a random matrix if we fix the genus and let q tends to infinity. There has been a lot of work recently on what happens to certain families if you fix q and let the genus tend to infinity. In particular, if you consider the family of curves such that K(C)/K is Galois and Gal(K(C)/K) is fixed, then it has been shown for several classes of groups that the number of points is distributed as a sum of q + 1 random variables. In this talk, we show this to be true if we fix Gal(K(C)/K) to be any abelian group.

MC 5479