On the Fundamental Group Scheme of Rationally Chain-Connected Varieties

Abstract : Let k be an algebraically closed field. Chambert-Loir proved that thé etale fundamental group of a proper normal rationally chain connected variety over k is finite. We prove that the fundamental group scheme of a proper normal rationally chain connected variety over k is finite too. In particular, the fundamental group scheme of a Fano variety is finite.
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Marco Antei, Indranil Biswas. On the Fundamental Group Scheme of Rationally Chain-Connected Varieties. International Mathematics Research Notices, Oxford University Press (OUP), 2015, 2016 (1), pp.311-324. ⟨10.1093/imrn/rnv132⟩. ⟨hal-01342088⟩

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