当前位置: X-MOL 学术J. Algebra › 论文详情
Our official English website, www.x-mol.net, welcomes your feedback! (Note: you will need to create a separate account there.)
A remark on connective K-theory
Journal of Algebra ( IF 0.8 ) Pub Date : 2020-10-01 , DOI: 10.1016/j.jalgebra.2020.06.015
Nikita A. Karpenko

Abstract Let X be a smooth algebraic variety over an arbitrary field. Let φ be the canonical surjective homomorphism of the Chow ring of X onto the ring associated with the Chow filtration on the Grothendieck ring K ( X ) . We remark that φ is injective if and only if the connective K-theory CK ( X ) coincides with the terms of the Chow filtration on K ( X ) . As a consequence, CK ( X ) turns out to be computed for numerous flag varieties (under semisimple algebraic groups) for which the injectivity of φ had already been established. This especially applies to the so-called generic flag varieties X of many different types, identifying for them CK ( X ) with the terms of the explicit Chern filtration on K ( X ) . Besides, for arbitrary X, we compare CK ( X ) with the fibered product of the Chow ring of X and the graded ring formed by the terms of the Chow filtration on K ( X ) .

中文翻译:

联结K理论评论

摘要 令 X 是任意域上的平滑代数变体。令 φ 是 X 的 Chow 环在与 Grothendieck 环 K (X) 上的 Chow 过滤相关的环上的规范满射同态。我们注意到 φ 是单射的,当且仅当连通性 K 理论 CK ( X ) 与 K ( X ) 上的 Chow 过滤项一致。因此,CK ( X ) 被证明是为已经建立 φ 的注入性的许多标志变体(在半单代数群下)计算的。这尤其适用于许多不同类型的所谓通用标志变体 X,用 K ( X ) 上的显式陈过滤条件为它们识别 CK ( X ) 。此外,对于任意 X,
更新日期:2020-10-01
down
wechat
bug