Brauer groups II: Twisted sheaves and applications
-- Max Lieblich

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This is the second part of a two part talk joint with Johan de Jong. We
introduce the period-index problem and describe its relation to
twisted sheaves, yielding a translation of the period-index problem
into a problem about the existence of rational points on the moduli
space of twisted sheaves.  We will then discuss these moduli spaces
for relative curves and show how their geometry can be used to prove
that period=index for Brauer classes on surfaces.  If time permits we
will indicate how to use the structure of the moduli spaces of twisted
sheaves on surfaces to study Brauer classes on surfaces over
non-algbraically closed base fields.  At the end
we hope to speculate on moduli of twisted sheaves in case the Brauer
class is ramified, as well as on the case of higher dimensional
varieties (e.g. threefolds).