Morita theory for non-commutative noetherian schemes

TL;DR

This paper explores Morita equivalences in non-commutative noetherian schemes, providing new proofs and criteria for equivalences of categories of sheaves and non-commutative curves.

Contribution

It offers a new proof of Caldararu's conjecture and establishes conditions for Morita equivalence of non-commutative curves.

Findings

New proof of Caldararu's conjecture

Necessary and sufficient conditions for Morita equivalence of non-commutative curves

Characterization of equivalences between categories of quasi-coherent sheaves

Abstract

In this paper, we study equivalences between the categories of quasi-coherent sheaves on non-commutative noetherian schemes. In particular, give a new proof of Caldararu's conjecture about Morita equivalences of Azumaya algebras on noetherian schemes. Moreover, we derive necessary and sufficient condition for two reduced non-commutative curves to be Morita equivalent.