Bounding generators for the kernel and cokernel of the tame symbol for curves

Abstract

Let $C$ be a regular, irreducible curve that is projective over a field. We obtain bounds in terms of the arithmetic genus of $C$ for the generators that are required for the cokernel of the tame symbol, as well as, under a simplifying assumption, its kernel. We briefly discuss a potential application to Chow groups.

Fixed a few typos and added minor clarifications. To appear in the special issue of Indagationes Mathematicae dedicated to the memory of Jacob Murre