Revista de la
Unión Matemática Argentina
Differential graded Brauer groups
Alexander Zimmermann

Volume 68, no. 1 (2025), pp. 297–308    

Published online (final version): May 28, 2025

https://doi.org/10.33044/revuma.4034

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Abstract

We consider central simple $K$-algebras which happen to be differential graded $K$-algebras. Two such algebras $A$ and $B$ are considered equivalent if there are bounded complexes of finite-dimensional $K$-vector spaces $C_A$ and $C_B$ such that the differential graded algebras $A\otimes_K \mathrm{End}_K^\bullet(C_A)$ and $B\otimes_K \mathrm{End}_K^\bullet(C_B)$ are isomorphic. Equivalence classes form an abelian group, which we call the dg Brauer group. We prove that this group is isomorphic to the ordinary Brauer group of the field $K$.

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