Abstract
In this paper we study the extension of structure group of principal bundles with a reductive algebraic group as structure group on a smooth projective variety defined over an algebraically closed field. Our main result is to show that given a finite-dimensional representation ρ of a reductive algebraic group G, there exists an integer N which is quantifiable in terms of G and ρ such that any semistable G-bundle whose first N Frobenius pullbacks are semistable induces a semistable bundle on extension of structure group via ρ. We do this by quantifying the fields of definition of the instability parabolics associated to various parabolic reductions of the induced bundle.
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GURJAR, S., MEHTA, V. RATIONALITY OF THE INSTABILITY PARABOLIC AND RELATED RESULTS. Transformation Groups 20, 99–112 (2015). https://doi.org/10.1007/s00031-014-9296-3
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DOI: https://doi.org/10.1007/s00031-014-9296-3