A geometric proof of a theorem of Serre

Date & time

4–5pm 23 September 2014


Building 27, Room G35


David Roberts (The University of Adelaide)


 Jack Hall

In about 1963 Serre wrote to Grothendieck "I looked at your problem on obstructions linked to the projective group and have come to the---rather surprising---conclusion that there is no counterexample...". Grothendieck then stated the theorem in Le groupe de Brauer I: every torsion $\mathbb{C}^\times$-gerbe on a compact space is the obstruction to lifting some bundle of Azumaya algebras to a vector bundle. Serre's proof proceeds by "...studying the topology of the classifying space of $PGL_n$, as $n \to \infty$". We give a new proof of this fact, inspired by Gabber's thesis, using geometric means: Azumaya bundles, gerbes and stacks.

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