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Cohen-Macaulay modules over two-dimensional graph orders

Klaus Roggenkamp — 1999

Colloquium Mathematicae

For a split graph order ℒ over a complete local regular domain 𝒪 of dimension 2 the indecomposable Cohen-Macaulay modules decompose - up to irreducible projectives - into a union of the indecomposable Cohen-Macaulay modules over graph orders of type •—• . There, the Cohen-Macaulay modules filtered by irreducible Cohen-Macaulay modules are in bijection to the homomorphisms ϕ : 𝒪 L ( μ ) 𝒪 L ( ν ) under the bi-action of the groups ( G l ( μ , 𝒪 L ) , G l ( ν , 𝒪 L ) ) , where 𝒪 L = 𝒪 / π for a prime π. This problem strongly depends on the nature of 𝒪 L . If 𝒪 L is regular,...

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