Abstract
Let k be an algebraic number field, (9k its ring of integers and V a non-empty open subscheme of Spec(Ck). Let X be a projective smooth geometrically irreducible scheme over k, and X a regular proper flat scheme over V such that X x Vk X. The purpose of this paper is to give an explicit description of the abelian fundamental ,ab (X) and 7T b(X), using some idele class groups attached to X and X by a K-theoretical method. Its outline is as follows: In general, for a noetherian scheme Z and i = 0 or 1, we define the group SKi(Z) to be the cokernel of
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