Geodesic
A note on certain Tannakian group schemes
Archivum mathematicum, Tome 56 (2020) no. 1, pp. 21-29.

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In this note, we prove that the $F$-fundamental group scheme is a birational invariant for smooth projective varieties. We prove that the $F$-fundamental group scheme is naturally a quotient of the Nori fundamental group scheme. For elliptic curves, it turns out that the $F$-fundamental group scheme and the Nori fundamental group scheme coincide. We also consider an extension of the Nori fundamental group scheme in positive characteristic using semi-essentially finite vector bundles, and prove that in this way, we do not get a non-trivial extension of the Nori fundamental group scheme for elliptic curves, unlike in characteristic zero.
DOI : 10.5817/AM2020-1-21
Classification : 14F05, 14L15
Keywords: F-fundamental group scheme; Frobenius-finite Vector bundles 
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Amrutiya, Sanjay. A note on certain Tannakian group schemes. Archivum mathematicum, Tome 56 (2020) no. 1, pp. 21-29. doi : 10.5817/AM2020-1-21. http://geodesic.mathdoc.fr/articles/10.5817/AM2020-1-21/

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