Martens, Johan

Thaddeus, Michael

English

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 genus zero with two marked points; (3) a gerbe over a football whose structure group is the nth roots of unity; (4) a line modulo an action of a split torus; (5) a chain of lines meeting in nodes; and (6) a chain modulo an action of a split torus. We also prove that the automorphism groups of such bundles are smooth, affine, and connected

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Variations on a theme of Grothendieck

https://www.pure.ed.ac.uk/ws/files/8188019/1210.8161v1

Variations on a theme of Grothendieck

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