Semistable principal $G$ -bundles in positive characteristic
Langer, Adrian
Duke Math. J., Tome 126 (2005) no. 1, p. 511-540 / Harvested from Project Euclid
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Let $X$ be a normal projective variety defined over an algebraically closed field $k$ of positive characteristic. Let $G$ be a connected reductive group defined over $k$ . We prove that some Frobenius pullback of a principal $G$ -bundle admits the canonical reduction $E_P$ such that its extension by $P\to P/R_u(P)$ is strongly semistable (see Theorem 5.1). ¶ Then we show that there is only a small difference between semistability of a principal $G$ -bundle and semistability of its Frobenius pullback (see Theorem 6.3). This and the boundedness of the family of semistable torsion-free sheaves imply the boundedness of semistable (rational) principal $G$ -bundles.
Publié le : 2005-06-15
Classification:  14D20,  14J60 
@article{1118341231,
     author = {Langer, Adrian},
     title = {Semistable principal $G$ -bundles in positive characteristic},
     journal = {Duke Math. J.},
     volume = {126},
     number = {1},
     year = {2005},
     pages = { 511-540},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1118341231}
}

Langer, Adrian. Semistable principal $G$ -bundles in positive characteristic. Duke Math. J., Tome 126 (2005) no. 1, pp.  511-540. http://gdmltest.u-ga.fr/item/1118341231/