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 ) .

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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，