Computing generators of the tame kernel of a global function field

The group K2 of a curve C over a finite field is equal to the tame kernel of the corresponding function field. We describe two algorithms for computing generators of the tame kernel of a global function field. The first algorithm uses the transfer map and the fact that the ℓ-torsion can easily be described if the ground field contains the ℓth roots of unity. The second method is inspired by an algorithm of Belabas and Gangl for computing generators of K2 of the ring of integers in a number field. We finally give the generators of the tame kernel for some elliptic function fields.