Preprint in the OpenAI Math release
A Complete Local Domain without a Small Cohen–Macaulay Module
OpenAI
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.
open until 1 Jan 2028
est. 50% chance this result is independently verified by the end of 2027.
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