We prove that any non-isotrivial elliptic K3 surface over an algebraically closed field of arbitrary characteristic contains infinitely many rational curves. This result was previously known in characteristic zero due to the work of Bogomolov and Tschinkel.

中文翻译：

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椭圆 K3 曲面上的有理曲线

我们证明了任意特征的代数闭域上的任何非等平凡椭圆 K3 曲面都包含无限多条有理曲线。由于 Bogomolov 和 Tschinkel 的工作，这个结果以前在特征零中是已知的。