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RESEARCH PRODUCT

Computing generators of the tame kernel of a global function field

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Abstract The group K 2 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 l th roots of unity. The second method is inspired by an algorithm of Belabas and Gangl for computing generators of K 2 of the ring of integers in a number field. We finally give the generators of the tame kernel for some elliptic function fields.