# A geometric proof of a theorem of Serre

## Date & time

4–5pm 23 September 2014

## Location

Building 27, Room G35

## Speakers

David Roberts (The University of Adelaide)

## Contacts

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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