Resumen de Differential graded Brauer groups

Alexander Zimmermann

• 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 CA and CB such that the differential graded algebras A ⊗K End• K(CA) and B ⊗K End• K(CB) 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.