The category of maximal Cohen--Macaulay modules as a ring with several objects
Henrik Holm
TL;DR
This paper investigates the category of maximal Cohen--Macaulay modules over a Cohen--Macaulay ring as a ring with several objects, extending known results to rings with arbitrary CM-type by computing its global dimension.
Contribution
It extends Leuschke's result by computing the global dimension for categories with arbitrary CM-type, viewing the module category as a ring with several objects.
Findings
Computed the global dimension of the category of maximal Cohen--Macaulay modules
Extended Leuschke's result to rings with arbitrary CM-type
Provided new insights into the structure of these categories
Abstract
Over a commutative local Cohen--Macaulay ring, we view and study the category of maximal Cohen--Macaulay modules as a ring with several objects. We compute the global dimension of this category and thereby extend a result of Leuschke to the case where the ring has arbitrary (as opposed to finite) CM-type.
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Commutative Algebra and Its Applications · Algebraic Geometry and Number Theory