Cohen-Macaulay modules over two-dimensional graph orders

Roggenkamp, Klaus

Colloquium Mathematicae, Tome 79 (1999), p. 25-48 / Harvested from The Polish Digital Mathematics Library

Résumé

For a split graph order ℒ over a complete local regular domain $\mathcal {O}$ 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 $ϕ : {{\mathcal {O}}}{L}^{(μ)} → {{\mathcal {O}}}{L}^{(ν)}$ under the bi-action of the groups $(Gl(μ,{{\mathcal {O}}}{L}),Gl(ν,{{\mathcal {O}}}{L}))$, where ${{\mathcal {O}}}{L} = \mathcal {O}/〈π〉$ for a prime π. This problem strongly depends on the nature of ${{\mathcal {O}}}{L}$. If ${{\mathcal {O}}}{L}$ is regular, then the category of indecomposable filtered Cohen-Macaulay modules is bounded. This latter condition is satisfied if ℒ is the completion of the Hecke order of the dihedral group of order 2p with p an odd prime at the maximal ideal 〈q-1,p〉, and more generally of blocks of defect p of complete Hecke orders. If ${{\mathcal {O}}}{L}$ is not regular, then the category of indecomposable filtered Cohen-Macaulay modules is unbounded.

Détail

Publié le : 1999-01-01

Zbl 0945.16013

EUDML-ID : urn:eudml:doc:210749

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