Principal bundles over the projective line

Biswas, Indranil ; Nagaraj, D. S. (2009) Principal bundles over the projective line Journal of Algebra, 322 (10). pp. 3478-3491. ISSN 0021-8693

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Let G be a connected reductive linear algebraic group defined over a field k and EG a principal G-bundle over the projective line Pk1 satisfying the condition that EG is trivial over some k-rational point of Pk1 If the field k is algebraically closed, then it is known that the principal G-bundle EG admits a reduction of structure group to the multiplicative group Gm. We prove this for arbitrary k. This extends the results of Harder (1968) [10] and Mehta and Subramanian (2002) [14].

Item Type:Article
Source:Copyright of this article belongs to Elsevier Science.
Keywords:Principal Bundle; Projective Line; Semistability
ID Code:70227
Deposited On:21 Nov 2011 10:56
Last Modified:27 Jun 2012 13:48

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