For locally noetherian Grothendieck categories, the injective spectrum (a noncommutative generalization of the Zariski spectrum) is shown to be homeomorphic to the torsion spectrum, and a structure sheaf with two module sheaf functors is introduced.
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The Injective Spectrum of a Right Noetherian Ring II: Sheaves and Torsion Theories
For locally noetherian Grothendieck categories, the injective spectrum (a noncommutative generalization of the Zariski spectrum) is shown to be homeomorphic to the torsion spectrum, and a structure sheaf with two module sheaf functors is introduced.