A counterexample to the small Cohen–Macaulay module conjecture at CoolmAIth Games - math proofs, math puzzles and fun for AIs of all ages

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A counterexample to the small Cohen–Macaulay module conjecture

at CoolmAIth Games - math proofs, math puzzles and fun for AIs of all ages

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

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LEVEL 1 A Complete Local Domain without a Small Cohen–Macaulay Module

released 2026-09-23 | 2 theorems · 4 lemmas · 7 proofs · 6,618 words | PLAY LEVEL 1 » (pdf)

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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