Cycles on Curves over Global Fields of Positive Characteristic
نویسنده
چکیده
Let k be a global field of positive characteristic, and let σ : X −→ Spec k be a smooth projective curve. We study the zero-dimensional cycle group V (X) = Ker(σ∗ : SK1(X) → K1(k)) and the one-dimensional cycle group W (X) = coker(σ∗ : K2(k) → H0 Zar(X,K2)), addressing the conjecture that V (X) is torsion and W (X) is finitely generated. The main idea is to use Abhyankar’s Theorem on resolution of singularities to relate the study of these cycle groups to that of the K-groups of a certain smooth projective surface over a finite field.
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