Monodromy group for a strongly semistable principal bundle over a curve

Biswas, Indranil ; Parameswaran, A. J. ; Subramanian, S. (2006) Monodromy group for a strongly semistable principal bundle over a curve Duke Mathematical Journal, 132 (1). pp. 1-48. ISSN 0012-7094

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Related URL: http://dx.doi.org/10.1215/S0012-7094-06-13211-8

Abstract

Let G be a semisimple linear algebraic group defined over an algebraically closed field k. Fix a smooth projective curve X defined over k, and also fix a closed point xεX. Given any strongly semistable principal G-bundle EG over X, we construct an affine algebraic group scheme defined over k, which we call the monodromy of EG. The monodromy group scheme is a subgroup scheme of the fiber over x of the adjoint bundle EG×GG for EG. We also construct a reduction of structure group of the principal G-bundle EG to its monodromy group scheme. The construction of this reduction of structure group involves a choice of a closed point of EG over x. An application of the monodromy group scheme is given. We prove the existence of strongly stable principal G-bundles with monodromy G.

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Deposited On:12 Oct 2010 04:26
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