## Duke Mathematical Journal

### Monodromy group for a strongly semistable principal bundle over a curve

#### 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 $x\in X$. Given any strongly semistable principal $G$-bundle $E_G$ over $X$, we construct an affine algebraic group scheme defined over $k$, which we call the monodromy of $E_G$. The monodromy group scheme is a subgroup scheme of the fiber over $x$ of the adjoint bundle $E_G\times^G G$ for $E_G$. We also construct a reduction of structure group of the principal $G$-bundle $E_G$ to its monodromy group scheme. The construction of this reduction of structure group involves a choice of a closed point of $E_G$ 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

#### 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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