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  "body": "\n## Statement\n\n- Serre's positivity conjecture that if $R$ is a commutative regular local ring, and $P, Q$ are [[prime ideals|00MHHZ9SNE]] of $R$, then $\\dim (R/P) + \\dim (R/Q) = \\dim (R)$ implies $\\chi(R/P, R/Q) \u003e 0$.\n",
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        "locator": "List of unsolved problems in mathematics, section Unsolved problems \u003e Algebra",
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  "name": "Serre's positivity conjecture",
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