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Let be a normal projective variety defined over an algebraically closed field of positive characteristic. Let be a connected reductive group defined over . We prove that some Frobenius pull back of a principal -bundle admits the canonical reduction such that its extension by is strongly semistable. Then we show that there is only a small difference between semistability of a principal -bundle and semistability of its Frobenius pull back. This and the boundedness of the family of semistable torsion free sheaves imply the boundedness of semistable principal -bundles.

生成讲解博客的中文版本

生成AI智能校验的中文版本