Let X be a quasicompact quasiseparated scheme. The collection of derived
Azumaya algebras in the sense of To\"en forms a group, which contains the
classical Brauer group of X and which we call Brβ (X) following
Lurie. To\"en introduced a map Ο:Brβ (X)βHet2β(X,Gmβ)
which extends the classical Brauer map, but instead of being injective, it is
surjective. In this paper we study the restriction of Ο to a subgroup
Br(X)βBrβ (X), which we call the "derived Brauer group", on
which Ο becomes an isomorphism Br(X)βHet2β(X,Gmβ). This
map may be interpreted as a derived version of the classical Brauer map which
offers a way to "fill the gap" between the classical Brauer group and the
cohomogical Brauer group. The group Br(X) was introduced by Lurie by making
use of the theory of prestable β-categories. There, the mentioned
isomorphism of abelian groups was deduced from an equivalence of
β-categories between the "Brauer space" of invertible presentable
prestable OXβ-linear categories, and the space Map(X,K(Gmβ,2)). We offer an alternative proof of this equivalence of
β-categories, characterizing the functor from the left to the right via
gerbes of connective trivializations, and its inverse via connective twisted
sheaves. We also prove that this equivalence carries a symmetric monoidal
structure, thus proving a conjecture of Binda an Porta.Comment: 23 page