Krull--Gabriel dimension of Cohen--Macaulay modules over hypersurfaces of countable Cohen--Macaulay representation type

2021/12/27 by Hiramatsu, Naoya
#Commutative Algebra (math.AC) #FOS: Mathematics #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.2112.13504

Abstract

We calculate the Krull--Gabriel dimension of the functor category of the (stable) category of maximal Cohen--Macaulay modules over hypersurfaces of countable Cohen--Macaulay representation type. We show that the Krull--Gabriel dimension is 0 if the hypersurface is of finite Cohen--Macaulay representation type and that is 2 if the hypersurface is of countable but not finite Cohen--Macaulay representation type.

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