On principal bundles over a projective varietydefined over a finite field

摘要

Let M be a geometrically irreducible smooth projective variety, defined over afinite field k, such that M admits a k—rational point xo. Let ω(M,x0) denotethe corresponding fundamental group—scheme introduced by Nori. Let EG bea principal G—bundle over M, where G is a reduced reductive linear algebraicgroup defined over the field k. Fix a polarization on M. We prove that thefollowing three statements are equivalent