### Extensions of Grothendieck's theorem on principal bundles over the projective line

**Thaddeus, M ***(Columbia)*

Tuesday 21 June 2011, 11:30-12:30

Seminar Room 2, Newton Institute Gatehouse

#### Abstract

Let G be a split reductive group over a field. Grothendieck and Harder proved that any principal G-bundle over the projective line reduces (essentially uniquely) to a maximal torus. In joint work with Johan Martens, we show that this remains true when the base is a chain of lines, a football, a chain of footballs, a finite abelian gerbe over any of these, or the stack-theoretic quotient of any of these by a torus action.

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