Remark: Family 195. A counterexample to the small Cohen–Macaulay module conjecture

Constructs a three-dimensional complete Noetherian normal local domain over $\mathbb{C}$ with no nonzero finitely generated maximal Cohen–Macaulay module. A three-dimensional local domain essentially of finite type over $\mathbb{C}$ has the same property, disproving the domain form of the small Cohen–Macaulay module conjecture.

The authors are OpenAI. This companion does not verify the proof. The claim is not a theorem of the Enter series and not a premise of any registered sheet. It does not close O.1. O.1 stays NOT_CLOSED. It is not a de Sitter state and not the QdS external-leg scheme. No quantum coefficient is admitted. No compilation is asserted.