On Cohen–Macaulay modules over the plane curve singularity of type $$\varvec{T_{44}}$$T44
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DOI: 10.1007/s00013-017-1034-3
Abstract: For a wide class of Cohen–Macaulay modules over the local ring of the plane curve singularity of type $$T_{44}$$T44, we explicitly describe the corresponding matrix factorizations. The calculations are based on the technique of matrix… read more here.
Keywords: cohen macaulay; curve singularity; singularity type; plane curve ... See more keywords
Integral perfectoid big Cohen–Macaulay algebras via André’s theorem
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DOI: 10.1007/s00208-018-1704-x
Abstract: The main result of this article is to prove that any Noetherian local domain of mixed characteristic maps to an integral perfectoid big Cohen–Macaulay algebra. The proof of this result is based on the construction… read more here.
Keywords: perfectoid big; cohen macaulay; macaulay; big cohen ... See more keywords
Geometry of varieties for graded maximal Cohen–Macaulay modules
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DOI: 10.1007/s00229-021-01282-x
Abstract: We study a variety for graded maximal Cohen–Macaulay modules, which was introduced by Dao and Shipman. The main result of this paper asserts that there are only a finite number of isomorphism classes of graded… read more here.
Keywords: graded maximal; maximal cohen; cohen macaulay; geometry ... See more keywords
The Structure of Chains of Ulrich Ideals in Cohen-Macaulay Local Rings of Dimension One
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DOI: 10.1007/s40306-018-0283-y
Abstract: This paper studies Ulrich ideals in one-dimensional Cohen-Macaulay local rings. A correspondence between Ulrich ideals and overrings is given. Using the correspondence, chains of Ulrich ideals are closely explored. The specific cases where the rings… read more here.
Keywords: cohen macaulay; macaulay local; chains ulrich; structure chains ... See more keywords
Partition and Cohen–Macaulay extenders
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DOI: 10.1016/j.ejc.2021.103488
Abstract: If a pure simplicial complex is partitionable, then its $h$-vector has a combinatorial interpretation in terms of any partitioning of the complex. Given a non-partitionable complex $\Delta$, we construct a complex $\Gamma \supseteq \Delta$ of… read more here.
Keywords: partition cohen; cohen macaulay; complex gamma; delta ... See more keywords
Applications and homological properties of local rings with decomposable maximal ideals
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DOI: 10.1016/j.jpaa.2018.06.006
Abstract: We construct a local Cohen-Macaulay ring $R$ with a prime ideal $\mathfrak{p}\in\spec(R)$ such that $R$ satisfies the uniform Auslander condition (UAC), but the localization $R_{\mathfrak{p}}$ does not satisfy Auslander's condition (AC). Given any positive integer… read more here.
Keywords: mathfrak; homological properties; cohen macaulay; local rings ... See more keywords
Maximal Cohen–Macaulay modules that are not locally free on the punctured spectrum
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DOI: 10.1016/j.jpaa.2020.106311
Abstract: We say that a Cohen-Macaulay local ring has finite $\operatorname{\mathsf{CM}}_+$-representation type if there exist only finitely many isomorphism classes of indecomposable maximal Cohen-Macaulay modules that are not locally free on the punctured spectrum. In this… read more here.
Keywords: cohen; cohen macaulay; representation type; mathsf representation ... See more keywords
Type and conductor of simplicial affine semigroups
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DOI: 10.1016/j.jpaa.2021.106844
Abstract: Abstract We provide a generalization of pseudo-Frobenius numbers of numerical semigroups to the context of the simplicial affine semigroups. In this way, we characterize the Cohen-Macaulay type of the simplicial affine semigroup ring K [… read more here.
Keywords: cohen macaulay; simplicial affine; affine semigroups; conductor ... See more keywords
Inequalities of invariants on Stanley–Reisner rings of Cohen–Macaulay simplicial complexes
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DOI: 10.1016/j.jpaa.2021.106888
Abstract: The goal of the present paper is the study of some algebraic invariants of Stanley–Reisner rings of Cohen–Macaulay simplicial complexes of dimension d − 1. We prove that the inequality d ≤ reg(∆) · type(∆)… read more here.
Keywords: cohen macaulay; macaulay simplicial; stanley reisner; reisner rings ... See more keywords
A note on semiorthogonal indecomposability of some Cohen-Macaulay varieties
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DOI: 10.1016/j.jpaa.2022.107076
Abstract: In this short note, we observe that the criterion proven in [KO15] for semiorthogonal indecomposability of the derived category of smooth DM stacks based on the canonical bundle can be extended to the case of… read more here.
Keywords: cohen macaulay; semiorthogonal indecomposability; note semiorthogonal; indecomposability cohen ... See more keywords
Higher generating subgroups and Cohen–Macaulay complexes
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DOI: 10.1017/s0013091519000415
Abstract: Abstract We show how to find higher generating families of subgroups, in the sense of Abels and Holz, for groups acting on Cohen–Macaulay complexes. We apply this to groups with a BN-pair to prove higher… read more here.
Keywords: higher generating; macaulay complexes; generating subgroups; cohen macaulay ... See more keywords