Abstract

We classify tilting classes over regular rings R of Krull dimension two. They are parametrized by the set of all pairs ( X , Y ) such that Ass R R ⊆ X ⊆ Spec ( R ) , Y consists of maximal ideals of height 2, and Y contains all the maximal ideals of height 2 that contain some element of X ∖ Ass R R . For R local, we also classify the corresponding infinitely generated tilting modules.

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