A geometric approach to noncommutative principal torus bundles (Q2840176)

The author introduces the concept of smooth localization of noncommutative algebras, which is motivated by the well-known localization of the commutative polynomial algebras arising in algebraic geometry. Using smooth localization, one can develop a classification theory of noncommutative principal torus bundles. One of the main features of the paper is the following beautiful theorem. Let \(A\) be an \(n\)-dimensional unital commutative algebra and \(M\) a smooth manifold. Then the spectrum of the algebra of sections of the noncommutative principal bundle over \(M\) is an \(n\)-fold covering of \(M\).