关于次K理论II的一个注记
A note on secondary K-theory II
摘要：
本文是[A note on secondary K-theory. Algebra and数论10（2016），no.4，887-906]。利用最近的非交换基模理论，证明了从导出Brauer群到次Grothendieck环的正则映射具有以下内射性：对于正则积分拟紧拟分离格式，它是内射的;在具有单个孤立奇点的积分正规诺特格式的情况下，它区分任何两个其差为无穷阶的导出Brauer类。作为应用，我们证明了正则映射在次数大于或等于4的光滑射影平面复曲线上的仿射锥以及Mumford奇异曲面上都是内射的.
英文摘要：
This note is the sequel to [A note on secondary K-theory. Algebra and Number Theory 10 (2016), no. 4, 887-906]. Making use of the recent theory of noncommutative motives, we prove that the canonical map from the derived Brauer group to the secondary Grothendieck ring has the following injectivity properties: in the case of a regular integral quasi-compact quasi-separated scheme, it is injective; in the case of an integral normal Noetherian scheme with a single isolated singularity, it distinguishes any two derived Brauer classes whose difference is of infinite order. As an application, we show that the canonical map is injective in the case of affine cones over smooth projective plane complex curves of degree greater than or equal to four as well as in the case of Mumford's (celebrated) singular surface.
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