关于Bloch-Quillen恒等式的Soulé变体的推广
On extending Soulé's variant of Bloch-Quillen identification
摘要：
基于Balmer的张量三角Chow群[2]，我们提出了方案的导出范畴的（Milnor）K-理论Chow群.这些Milnor K-理论Chow群恢复了经典的Chow群[6]，并且可以检测幂零，而经典的Chow群不能。作为一个应用，我们扩展Soulé的变体Bloch Quilled识别光滑的投射品种，他们平凡的无穷小加厚。这肯定地回答了Green-Griffiths关于微小变形的问题，参见下面的问题1.1。
英文摘要：
Based on Balmer's tensor triangular Chow group [2], we propose (Milnor)K-theoretic Chow groups of derived categories of schemes. These Milnor K-theoretic Chow groups recover the classical ones [6] for smooth projective varieties and can detect nilpotent, while the classical ones can't do. As an application, we extend Soulé's variant of Bloch-Quilled identification from smooth projective varieties to their trivial infinitesimal thickenings. This answers affirmatively a question by Green-Griffiths for trivial deformations, see Question 1.1 below.
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