Duke Mathematical Journal

Monodromy group for a strongly semistable principal bundle over a curve

Indranil Biswas, A. J. Parameswaran, and S. Subramanian

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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

Article information

Source
Duke Math. J., Volume 132, Number 1 (2006), 1-48.

Dates
First available in Project Euclid: 28 February 2006

Permanent link to this document
https://projecteuclid.org/euclid.dmj/1141136435

Digital Object Identifier
doi:10.1215/S0012-7094-06-13211-8

Mathematical Reviews number (MathSciNet)
MR2219253

Zentralblatt MATH identifier
1106.14032

Subjects
Primary: 14L15: Group schemes 14L17: Affine algebraic groups, hyperalgebra constructions [See also 17B45, 18D35]
Secondary: 14H60: Vector bundles on curves and their moduli [See also 14D20, 14F05]

Citation

Biswas, Indranil; Parameswaran, A. J.; Subramanian, S. Monodromy group for a strongly semistable principal bundle over a curve. Duke Math. J. 132 (2006), no. 1, 1--48. doi:10.1215/S0012-7094-06-13211-8. https://projecteuclid.org/euclid.dmj/1141136435


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