Noncommutative Projective Schemes

Abstract

An analogue of the concept of projective scheme is defined for noncommutative N-graded algebras using the quotient category C of graded right A-modules modulo its full subcategory of torsion modules. We define proj A = (C, A, s), where A is the object corresponding to the module AA, and s is the autoequivalence defined by the shift of degrees. The triples equivalent to proj A for a right noetherian graded algebra A are characterized in terms of a condition χ on extensions. © 1994 Academic Press. All rights reserved.