Amrutiya, SanjaySanjayAmrutiya2025-08-312025-08-312020-01-0110.5817/AM2020-1-212-s2.0-85084378169https://d8.irins.org/handle/IITG2025/24281In 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.trueF-fundamental group scheme | Frobenius-finite Vector bundlesArticlehttp://dml.cz/bitstream/handle/10338.dmlcz/148033/ArchMathRetro_056-2020-1_3.pdf1212505921-2920201arJournal1