Abstract
Let be a semisimple linear algebraic group defined over an algebraically closed field . Fix a smooth projective curve defined over , and also fix a closed point . Given any strongly semistable principal -bundle over , we construct an affine algebraic group scheme defined over , which we call the monodromy of . The monodromy group scheme is a subgroup scheme of the fiber over of the adjoint bundle for . We also construct a reduction of structure group of the principal -bundle to its monodromy group scheme. The construction of this reduction of structure group involves a choice of a closed point of over . An application of the monodromy group scheme is given. We prove the existence of strongly stable principal -bundles with monodromy
Citation
Indranil Biswas. A. J. Parameswaran. S. Subramanian. "Monodromy group for a strongly semistable principal bundle over a curve." Duke Math. J. 132 (1) 1 - 48, 15 March 2006. https://doi.org/10.1215/S0012-7094-06-13211-8
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