Abstract
The main goal of this paper is to give a description of the abelian étale fundamental group of a smooth (not necessarily proper) variety U over a p-adic field k in case that U has a smooth compactification that has good reduction over k. The group SK1 in the proper case is replaced with motivic homology. Certain isomorphisms between motivic homology and the abelian étale fundamental groups are established by using known results on vanishing of Kato homology.
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