Two definable subcategories of maximal Cohen-Macaulay modules

2019/04/18 by Bird, Isaac · 1 citation
#13C11 #13C14 #13D07 #13L05 #Commutative Algebra (math.AC) #FOS: Mathematics #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.1904.08687

Abstract

Over a Cohen-Macaulay ring we consider two extensions of the maximal Cohen-Macaulay modules from the viewpoint of definable subcategories, which are closed under direct limits, direct products and pure submodules. After describing these categories, we compare them and consider which properties they inherit from the maximal Cohen-Macaulay modules. We then consider some further properties of these classes and how they interact with the entire module category.

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• Govorov--Lazard and finite deconstructibility for Gorenstein and restricted homological dimensions

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