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15 March 2006 Monodromy group for a strongly semistable principal bundle over a curve
Indranil Biswas, A. J. Parameswaran, S. Subramanian
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Duke Math. J. 132(1): 1-48 (15 March 2006). DOI: 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 xX. 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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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

Information

Published: 15 March 2006
First available in Project Euclid: 28 February 2006

zbMATH: 1106.14032
MathSciNet: MR2219253
Digital Object Identifier: 10.1215/S0012-7094-06-13211-8

Subjects:
Primary: 14L15, 14L17
Secondary: 14H60

Rights: Copyright © 2006 Duke University Press

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Vol.132 • No. 1 • 15 March 2006
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