Extension of structure groups of principal bundles in positive characteristic

Details Extension of structure groups of principal bundles in positive characteristic Extension of structure groups of principal bundles in positive characteristic

2003-12-14

arxiv.org/abs/math/0312280v2

Mathematics

Algebraic Geometry

25 pages. To appear in the J. Reine Angew. Math

Scientific paper

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 \cite{Ramanan-Ramanathan} 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.

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