We prove that isogenous K3 surfaces have isomorphic Chow motives. This provides a motivic interpretation of a long standing conjecture of Safarevich which has been settled only recently by Buskin. The main step consists of a new proof of Safarevich's conjecture that circumvents the analytic parts in Buskin's approach, avoiding twistor spaces and non-algebraic K3 surfaces.

中文翻译：

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同质 K3 表面的动机

我们证明同构 K3 表面具有同构 Chow 动机。这为萨法列维奇的一个长期存在的猜想提供了动机解释，该猜想最近才由布斯金解决。主要步骤包括对 Safarevich 猜想的新证明，该猜想绕过了 Buskin 方法中的解析部分，避免了扭曲空间和非代数 K3 曲面。