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started Brauer group, collecting some references on the statement that/when $Br(X) \simeq H^2_{et}(X, \mathbb{G}_m)_{tor}$ and moved notes from a talk by David Gepner on $\infty$-Brauer groups to there.
I added the insightful references of Street at Azumaya algebra and at Brauer group:
Thanks. I have changed “Brower group” to “Brauer group”, okay?
So I have added a remark in a new section Relation to categories of modules.
Thanks for Brauer, Urs.
added to Brauer group references on Brauer groups for superalgebras.
added Duskin’s historical paper
have added to Brauer group a paragraph (here) on its “bigger” version (thanks toDavid C. for the pointer to Heinloth’s article)
It is therefore natural to regard all of $H^2_{et}(R, \mathbb{G}_m)$ as the “actual” Brauer group. This has been called the “bigger Brauer group” (Taylor 82, Caenepeel-Grandjean 98, Heinloth-Schöer 08). the bigger Brauer group has actually traditionally been implicit already in the term “formal Brauer group”, which is really the formal geometry-version of the bigger Brauer group.
Have added at the references at Brauer group:
The observation that passing to derived algebraic geometry makes also the non-torsion elements in $H^2_{et}(-,\mathbb{G}_m)$ be represented by (derived) Azumaya algebras is due to
- {#Toen10} Bertrand Toën, Derived Azumaya algebras and generators for twisted derived categories (arXiv:1002.2599)
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