In mathematics, a Nori semistable vector bundle is a particular type of vector bundle whose first definition has been first implicitly suggested by Madhav V. Nori,[1][2] as one of the main ingredients for the construction of the fundamental group scheme.
Also, Nori's definition was different from the one suggested nowadays.
[3] The category of Nori semistable vector bundles contains the Tannakian category of essentially finite vector bundles, whose naturally associated group scheme is the fundamental group scheme
is Nori semistable if for any smooth and proper curve
[4] Nori semistable vector bundles were called by Nori semistable causing a lot of confusion with the already existing definition of semistable vector bundles.
More importantly Nori simply said that the restriction of
Then for instance in positive characteristic a morphism
like the Frobenius morphism was not included in Nori's original definition.
The importance of including it is that the above definition makes the category of Nori semistable vector bundles tannakian and the group scheme associated to it is the
Instead, Nori's original definition didn't give rise to a Tannakian category but only to an abelian category.
This algebraic geometry–related article is a stub.