Extension of structure groups of principal bundles in positive characteristic
- 1 January 2006
- journal article
- research article
- Published by Walter de Gruyter GmbH in Journal für die reine und angewandte Mathematik (Crelles Journal)
- Vol. 2006 (595) , 1-24
- https://doi.org/10.1515/crelle.2006.042
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.Keywords
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