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arXiv · 1410.1166

On the fundamental group scheme of rationally chain connected varieties

Marco Antei·Indranil Biswas
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Abstract

Let $k$ be an algebraically closed field. Chambert-Loir proved that the étale fundamental group of a normal rationally chain connected variety over $k$ is finite. We prove that the fundamental group scheme of a normal rationally chain connected variety over $k$ is finite and étale. In particular, the fundamental group scheme of a Fano variety is finite and étale.

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Marco Antei, Indranil Biswas. 2015-05-21. On the fundamental group scheme of rationally chain connected varieties. https://doi.org/10.1093/imrn%2Frnv132

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