Let X be an affine, simplicial, split toric variety over a field. Let G 0 denote the Grothendieck group of coherent sheaves on a Noetherian scheme and let F 1 G 0 denote the first step of the filtration on G 0 by codimension of support. Then G 0 ( X ) ≅ Z ⊕ F 1 G 0 ( X ) and F 1 G 0 ( X ) is a finite abelian group. In dimension 2, we show that F 1 G 0 ( X ) is a finite cyclic group and determine its order. In dimension 3, F 1 G 0 ( X ) is determined up to a group extension of the Chow group A 1 ( X ) by the Chow group A 2 ( X ) . We determine the order of the Chow group A 1 ( X ) in all dimensions. A conjecture on the order of A 2 ( X ) is formulated for all dimensions.
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