Essentially finite vector bundle
In mathematics, an essentially finite vector bundle is a particular type of vector bundle defined by Madhav Nori,[1][2] as the main tool in the construction of the fundamental group scheme. Even if the definition is not intuitive there is a nice characterization that makes essentially finite vector bundles quite natural objects to study in algebraic geometry. So before recalling the definition we give this characterization:
Characterization
Let be a reduced and connected scheme over a perfect field
endowed with a section
. Then a vector bundle
over
is essentially finite if and only if there exists a finite
-group scheme
and a
-torsor
such that
becomes trivial over
(i.e.
, where
).