# Variations on a theme of Grothendieck

@article{Martens2012VariationsOA, title={Variations on a theme of Grothendieck}, author={Johan Martens and Michael Thaddeus}, journal={arXiv: Algebraic Geometry}, year={2012} }

Grothendieck and Harder proved that every principal bundle over the projective line with split reductive structure group (and trivial over the generic point) can be reduced to a maximal torus. Furthermore, this reduction is unique modulo automorphisms and the Weyl group. In a series of six variations on this theme, we prove corresponding results for principal bundles over the following schemes and stacks: (1) a line modulo the group of nth roots of unity; (2) a football, that is, an orbifold of…

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