{"id":"openai-math/Positivity-of-Serres-Intersection-Multiplicity","pdf":"https://github.com/openai/math/blob/main/preprints/Positivity-of-Serres-Intersection-Multiplicity-September-23-2026/paper.pdf","url":"https://github.com/openai/math/tree/main/preprints/Positivity-of-Serres-Intersection-Multiplicity-September-23-2026","tags":["commutative-algebra","algebraic-geometry","intersection-theory"],"score":0,"title":"Positivity of Serre's Intersection Multiplicity","domain":"Algebra","family":"193","origin":"ai-generated","source":"openai-math","authors":["OpenAI"],"reviews":0,"subject":"math.RA","summary":"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.","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"discussed":0,"published":"2026-09-23","reactions":{},"formalized":false,"family_title":"Serre’s intersection-multiplicity conjecture"}