2011/11/11 by Gurjar, Sudarshan, Mehta, Vikram
#14J60 #14L24 #Algebraic Geometry (math.AG) #FOS: Mathematics
paper · doi:10.48550/arxiv.1111.2799
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 ρ 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 ρ. Moreover we quantify the number of such frobenius pullbacks required.