Amrutiya, SanjaySanjayAmrutiya2025-08-282025-08-282018-10-01http://arxiv.org/abs/1810.10027https://d8.irins.org/handle/IITG2025/20044In this note, we prove that the F-fundamental group scheme is 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 coincides. 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.en-USAlgebraGeometryAlgebraic Geometrye-Printe-Print123456789/555