Speaker: Jeremy Booher, University of Florida

Title: Towers of Curves, Motivic Class Groups, and Equicharacteristic
L-Functions

Abstract:  For a prime p, let K_n form a Z_p-tower of function fields
corresponding to smooth projective curves C_n over a perfect field of
characteristic p. The genus is a well-understood invariant of
algebraic curves, and the genus of C_n depends on n in a simple
fashion. In characteristic p, there are additional curve invariants
like the a-number which are poorly understood. They describe the
group-scheme structure of the p-torsion of the Jacobian of C_n, a
geometric generalization of the class group of K_n. I will describe
work with Bryden Cais, Joe Kramer-Miller, and James Upton which shows
that the a-number and more generally p-part of the “motivic class
group” of C_n depends regularly on n. We do so using an
equicharacteristic L-function.