OPENAI MATHEMATICS COLLECTION · FAMILY 195
A Complete Local Domain without a Small Cohen–Macaulay Module
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Abstract
We construct a three-dimensional complete Noetherian normal local domain containing ℂ, with residue field ℂ, that has no nonzero finitely generated maximal Cohen–Macaulay module. This disproves the domain form of the small Cohen–Macaulay module conjecture.
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