On principal bundles over a projective variety defined over a finite field

Publisher： Cambridge University Press

E-ISSN： 1865-5394|4|2|209-221

ISSN： 1865-2433

Source： Journal of K-Theory, Vol.4, Iss.2, 2009-10, pp. : 209-221

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Abstract

Let M be a geometrically irreducible smooth projective variety, defined over a finite field k, such that M admits a k-rational point x0. Let (M,x0/ denote the corresponding fundamental group-scheme introduced by Nori. Let EG be a principal G-bundle over M, where G is a reduced reductive linear algebraic group defined over the field k. Fix a polarization ξ on M. We prove that the following three statements are equivalent:

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