Rationality of the instability parabolic and related results
Abstract
In this paper we study the extension of structure group of principal bundles with a reductive algebraic group as structure group on smooth projective varieties defined over algebraically closed field of positive characteristic. Our main result is to show that given a representation of a reductive algebraic group G, there exists an integer t such that any semistable G-bundle whose first t frobenius pullbacks are semistable induces a semistable vector bundle on extension of structure group via . Moreover we quantify the number of such frobenius pullbacks required.
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