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arXiv · 1604.04046

On extending Soul\'e's variant of Bloch-Quillen identification

Sen Yang
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Abstract

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 Soul\'e'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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Sen Yang. 2016-04-14. On extending Soul\'e's variant of Bloch-Quillen identification. https://arxiv.org/abs/1604.04046

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