Morita theory for non-commutative noetherian schemes

In this paper, we study equivalences between the categories of quasi-coherent sheaves on non-commutative noetherian schemes. In particular, we give a new proof of Caldararu's conjecture about Morita equivalences of Azumaya algebras on noetherian schemes. Moreover, we derive necessary and suf-ficient condition for two reduced non-commutative curves to be Morita equivalent. (c) 2022 Elsevier Inc. All rights reserved.