Biswas, Indranil ; Parameswaran, A. J.
(2008)
*Monodromy group for a strongly semistable principal bundle over a curve. II*
Journal of K-Theory, 1
(3).
pp. 583-607.
ISSN 1865-2433

Full text not available from this repository.

Official URL: http://journals.cambridge.org/action/displayAbstra...

Related URL: http://dx.doi.org/10.1017/is007011017jkt015

## Abstract

Let X be a geometrically irreducible smooth projective curve defined over a field k. Assume that X has a k-rational point; fix a k-rational point x ε X. From these data we construct an affine group scheme X defined over the field k as well as a principal X-bundle S1755069607000151inline1 over the curve X. The group scheme X is given by a xs0211A-graded neutral Tannakian category built out of all strongly semistable vector bundles over X. The principal bundle S1755069607000151inline1 is tautological. Let G be a linear algebraic group, defined over k, that does not admit any nontrivial character which is trivial on the connected component, containing the identity element, of the reduced center of G. Let E_{G} be a strongly semistable principal G-bundle over X. We associate to E_{G} a group scheme M defined over k, which we call the monodromy group scheme of E_{G}, and a principal M-bundle E_{M} over X, which we call the monodromy bundle of E_{G}. The group scheme M is canonically a quotient of X, and E_{M} is the extension of structure group of S1755069607000151inline1. The group scheme M is also canonically embedded in the fiber Ad(E_{G})_{x} over x of the adjoint bundle.

Item Type: | Article |
---|---|

Source: | Copyright of this article belongs to Cambridge University Press. |

Keywords: | Neutral Tannakian Category; Principal Bundle; Semistability |

ID Code: | 35418 |

Deposited On: | 04 Jul 2012 13:30 |

Last Modified: | 04 Jul 2012 13:30 |

Repository Staff Only: item control page