Remarks on rational points of varieties whose cotangent bundles are generated by global sections

In this short note, we will give several remarks on rational points of varieties whose cotangent bundles are generated by global sections. For example, we will show that if the sheaf of differentials $\Omega^1_{X/k}$ of a projective variety $X$ over a number field $k$ is ample and generated by global sections, then the set of $k$-rational points of $X$ is finite.

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Published 1 January 1995