On the Fundamental Group Scheme of Rationally Chain-Connected Varieties

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,...

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Veröffentlicht in:	International mathematics research notices 2016-01, Vol.2016 (1), p.311-324
Hauptverfasser:	Antei, Marco, Biswas, Indranil
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Sprache:	eng
Schlagworte:	Mathematics
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creator	Antei, Marco Biswas, Indranil
description	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.
doi_str_mv	10.1093/imrn/rnv132
format	Article
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title	On the Fundamental Group Scheme of Rationally Chain-Connected Varieties
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