A note on the non-existence of small Cohen-Macaulay algebras
classification
🧮 math.AC
math.AG
keywords
cohen-macaulayexamplesadmitalgebrasalwayscharacteristiccompleteconstruct
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By finding a p-adic obstruction, we construct many examples of positive characteristic complete noetherian local rings which do not admit any module-finite Cohen-Macaulay extension. These examples should be contrasted with a result of Hochster-Huneke: the union of all finite extensions is always Cohen-Macaulay.
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