In our previous paper (Commun. Algebra, 45(8)
(2017) 3422–3448), we studied the category of semifinite bundles on a proper variety defined over a field of characteristic 0. As a result, we obtained the fact that for a smooth projective curve defined over an algebraically closed field of characteristic 0 with genus \(g>1\), Nori fundamental group acts faithfully on the unipotent fundamental group of its universal covering. However, it was not mentioned about any explicit module structure. In this paper, we prove that the Chevalley–Weil formula gives a description of it.
Fundamental group schemes vector bundles Tannaka duality
Mathematics Subject Classification
14L15 14H30 14H60
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The author would like to thank Professor Takao Yamazaki for many discussions clarifying the relation between his previous work and the Chevalley–Weil formula. The author also thanks Professor Takuya Yamauchi for suggesting many examples of projective smooth higher dimensional varieties with infinitely abelian fundamental group. The author is supported by JSPS, Grant-in-Aid for Scientific Research for JSPS fellows (16J02171).
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