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arXiv math/06011752006-01-09math.AGmath.KT

Milnor-Chow同态的再研究

The Milnor-Chow homomorphism revisited

Moritz Kerz, Stefan Müller-Stach

备注：: 8 pages

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摘要：

本文的目的是对具有$k$无穷大的本质光滑（半）局部$k$ -代数$A$给出Milnor $K$ -理论与高阶Chow群之间的自然Milnor-Chow同态$ρ: K^M_n(A) \to CH^n(A,n)$满射性的一个简化证明.它暗示了Milnor $K$ -理论在泛点的Gersten分解的精确性。我们的方法使用了Bloch-Levine移动技巧和Milnor $K$ -理论范数的一些性质。

英文摘要：

The aim of this note is to give a simplified proof of the surjectivity of the natural Milnor-Chow homomorphism $ρ: K^M_n(A) \to CH^n(A,n)$ between Milnor $K$-theory and higher Chow groups for essentially smooth (semi-)local $k$-algebras $A$ with $k$ infinite. It implies the exactness of the Gersten resolution for Milnor $K$-theory at the generic point. Our method uses the Bloch-Levine moving technique and some properties of the Milnor $K$-theory norm for fields.

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