Divisibility of function field class
numbers
Jeff Achter
Given an elliptic curve over a finite field, one might ask for the chance that it has a rational point of order $\ell$. More generally, what is the chance that a curve drawn from a family over a finite field has a point of order $\ell$ on its Jacobian?
The answer is encoded in the $\ell$-adic monodromy representation of the family in question. In this talk, I'll discuss recent work on this representation for various families of curves, and use it to prove a Cohen-Lenstra-type result for class groups of function fields.