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Indecomposable Cohen-Macaulay modules and irreducible maps

In: Algebraic Geometry

Author

Listed:
  • Dorin Popescu

    (INCREST, Dept. of Math.)

  • Marko Roczen

    (Humboldt-Universität, Sekt. Mathematik)

Abstract

Let (R, m) be a local CM-ring and M a finitely generated (shortly f.g.) R-module. M is a maximal CM module (shortly MCM R-modules. The isomorphism classes of indecomposable MCM R-modules form the vertices of the Auslander-Reiter quiver Γ(R) of R. Section 3 studies the behaviour of Γ(R) under base change; best results (cf. (3.10), (3.14)) being partial answers to the conjectures from [Sc] (7.3). Unfortunately, the proofs use the difficult theory of Artin approximation (cf. [Ar], or [Pol]).

Suggested Citation

  • Dorin Popescu & Marko Roczen, 1990. "Indecomposable Cohen-Macaulay modules and irreducible maps," Springer Books, in: H. Kurke & J. H. M. Steenbrink (ed.), Algebraic Geometry, pages 277-294, Springer.
    • Handle: RePEc:spr:sprchp:978-94-009-0685-3_14
    DOI: 10.1007/978-94-009-0685-3_14
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