A criterion for the strongly semistable principal bundles over a curve in positive characteristic

Biswas, Indranil ; Parameswaran, A. J. (2004) A criterion for the strongly semistable principal bundles over a curve in positive characteristic Bulletin des Sciences Mathematiques, 128 (9). 761 -773. ISSN 0007-4497

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Official URL: http://linkinghub.elsevier.com/retrieve/pii/S00074...

Related URL: http://dx.doi.org/10.1016/j.bulsci.2004.03.013

Abstract

Let X be an irreducible smooth projective curve over an algebraically closed field k of positive characteristic and G a simple linear algebraic group over k. Fix a proper parabolic subgroup P of G and a nontrivial anti-dominant character λ of P. Given a principal G-bundle EG over X, let EG(λ) be the line bundle over EG/P associated to the principal P-bundle EG→EG/P for the character λ. We prove that EG is strongly semistable if and only if the line bundle EG(λ) is numerically effective. For any connected reductive algebraic group H over k, a similar criterion is proved for strongly semistable H-bundles.

Item Type:Article
Source:Copyright of this article belongs to Elsevier Science.
Keywords:Principal Bundle; Semistable Bundle; Numerically Effectiveness
ID Code:35222
Deposited On:04 Jul 2012 13:27
Last Modified:04 Jul 2012 13:27

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