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Fields with vanishing K2. Torsion in H1(X, K2) and Ch2(x)

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Abstract

This paper describes fields F of nonzero characteristic with the property that for all finite extensions E/F K2E=0. We consider a somewhat wider class of fields which includes finite and separably closed fields. For smooth projective varieties X over such a field we show that the groups H1(X, K2){ℓ} and H2(Xet, ℚℓ∣ℤℓ(2)), NH3(Xet, ℚℓ∣ℤℓ(2)) and Ch2(X){ℓ} are isomorphic. These results are applied to describe the groups SK1 of a smooth affine curve over such a field.

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Authors
  1. I. A. Panin
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Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 116, pp. 108–118, 1982.

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Panin, I.A. Fields with vanishing K2. Torsion in H1(X, K2) and Ch2(x). J Math Sci 26, 1901–1908 (1984). https://doi.org/10.1007/BF01670578

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