A sufficient condition for the almost Cohen–Macaulayness of the absolute integral closure in dimension 4

Tavanfar, Ehsan

doi:10.1080/00927872.2017.1392539

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Cited by 2 publications

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“…For a given complete local domain (R, m), can one find a module-finite domain extension R → S such that S is normal and quasi-Gorenstein? [T18,Theorem 2.5], an analogue of this problem has an affirmative answer. Namely, when the (R 1 )-condition (because of normality) is replaced with the condition of being locally complete intersection in codimension ≤ 1.…”

Section: Introductionmentioning

confidence: 99%

On local rings without small Cohen-Macaulay algebras in mixed characteristic

Shimomoto¹,

Tavanfar²

2021

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For any d ≥ 4, we prove that there are examples of (complete or excellent) d-dimensional mixed characteristic normal local rings admitting no small Cohen-Macaulay algebra. We give two different proofs. While the first proof is not constructive, the second one gives an explicit example based on an example constructed by B. Bhatt. Moreover, it is shown that our explicit example admits a small Cohen-Macaulay module even though it does not admit a small Cohen-Macaulay algebra.

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Section: Introductionmentioning

confidence: 99%