{"id":"openai-math/P-equals-W-in-composite-rank-for-fixed-determinant","pdf":"https://github.com/openai/math/blob/main/preprints/P-equals-W-in-composite-rank-for-fixed-determinant-September-24-2026/P-equals-W-in-composite-rank-for-fixed-determinant-September-24-2026.pdf","url":"https://github.com/openai/math/tree/main/preprints/P-equals-W-in-composite-rank-for-fixed-determinant-September-24-2026","tags":["algebraic-geometry","higgs-bundles","mixed-hodge-theory"],"score":0,"title":"P=W in composite rank for fixed determinant","domain":"Algebraic and complex geometry","family":"043","origin":"ai-generated","source":"openai-math","authors":["OpenAI"],"reviews":0,"subject":"math.AG","summary":"We prove the P = W conjecture on the full rational cohomology of fixed-determinant, trace-free Higgs moduli spaces in composite rank and coprime degree, for smooth projective complex curves of genus at least two. Together with the established prime-rank cases, this gives the equality in every coprime rank.","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"discussed":0,"published":"2026-09-24","reactions":{},"formalized":false,"family_title":"P = W for fixed-determinant SL n moduli spaces"}