Algebra·OpenAI Math·Result 193
Serre’s intersection-multiplicity conjecture
One of the 372 results in OpenAI's public mathematics catalogue, filed under algebra: 1 preprint, the latest dated 23 September 2026. This page quotes OpenAI's own summary of the claim, links the paper and abstract, and will embed the animation.
Latest paper
Positivity of Serre's Intersection Multiplicity
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What OpenAI claims
Proves strict positivity of Serre's intersection multiplicity χR(M,N) for nonzero finitely generated modules over any regular local ring, provided M⊗R N has finite length and dim M+dim N=dim R. This resolves the positivity conjecture, including ramified mixed characteristic.
Paper
Positivity of Serre's Intersection Multiplicity
We prove Serre's positivity conjecture, including ramified mixed characteristic. If two nonzero finitely generated modules over a regular local ring have tensor product of finite length and complementary dimensions, then their intersection multiplicity is strictly positive.
Status
Preprint. The paper has not been independently reviewed. Treat the result as OpenAI's claim until other mathematicians have checked it. If a video exists, it illustrates the statement; it is not the proof.
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