Extension of structure groups of principal bundles in positive characteristic

Abstract

In this article we study the behaviour of semistable principal G-bundles over a smooth projective variety X under the extension of structure groups in positive characteristic. We extend some results of Ramanan-Ramanathan [S. Ramanan and A. Ramanathan, Some remarks on the instability flag, Tohoku Math. J. 36 (1984), 269–291.] on rationality of instability flags and show that the associated vector bundles via representations of G are not too unstable and the instability can be bounded by a constant independent of semistable bundles. As a consequence of this the boundedness of the set of isomorphism classes of semistable G-bundles with fixed degree and Chern classes is proven.