Milnor <i>K</i>-theory of Smooth Varieties期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

Milnor K-theory of Smooth Varieties

Authors:	Reza Akhtar

Affiliation:	(1) Department of Mathematics and Statistics, Miami University, Oxford, OH 45056, USA

Abstract:	Let k be a field and X a smooth projective variety of dimension d over k. Generalizing a construction of Kato and Somekawa, we define a Milnor-type group $K_s(k;{{cal CH} _0} (X); {{bf G} } _m)$ which is isomorphic to the ordinary Milnor $K$-group $K_s^m(k)$ in the case $X={Spec~} k$ We prove that $K_s(k; {{cal CH} _0} (X); {{bf G} } _m)$ is isomorphic to both the higher Chow group CH^d+s (X,s) and the Zariski cohomology group $H_{Zar} ^d(X, {{cal K} } ^M_{d+s} )$

Keywords:	Milnor K-group higher Chow group mixed K-group zero-dimensional cycles
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