| Résume | Résumé: Often, Hodge theory suggests that there is a link between the Brauer group of a variety
and the Brauer group of the moduli space of sheaves on that variety. Making this explicit
is, however, not immediate. I will discuss the case of moduli spaces of sheaves on
K3 surfaces and explain how this leads to a period-index conjecture for unramified
Brauer classes on hyperkähler manifolds which can be verified in certain cases.
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