Brauer groups I: moduli of Azumaya algebras
-- Johan de Jong

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This is the first of a two part talk joint with Max Lieblich. In this
talk we briefly recall
the relationship between the cohomological Brauer group and the Brauer
group of a scheme. We explain this relationship geometrically in terms of
twisted sheaves, and discuss how viewing things from this perspective
can help prove equality of the two
Brauer groups for quasi-projective schemes.  After this we describe a
compactification of the moduli space of Azumaya algebras in terms of
generalized
Azumaya algebras, which are "algebras in the derived category.''
This compactification has many formal similarities to the moduli space
of semistable sheaves, some of which will be discussed in the second
lecture.