Duke Mathematical Journal
- Duke Math. J.
- Volume 132, Number 1 (2006), 1-48.
Monodromy group for a strongly semistable principal bundle over a curve
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
Duke Math. J., Volume 132, Number 1 (2006), 1-48.
First available in Project Euclid: 28 February 2006
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Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
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]
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