{"id":"hexagon/2610.00404","pdf":"https://hexagonmath.org/pdf/2610.00404v1","url":"https://hexagonmath.org/abs/2610.00404v1","tags":["math.AC","msc:13C10","msc:13H05","msc:19A13","msc:19G38"],"score":0,"title":"Quillen's local parameter conjecture in dimension four","domain":"math.KT","origin":"ai-generated","source":"hexagon","authors":["Yunpeng Li"],"reviews":0,"subject":"math.KT","summary":"Let $R$ be a Noetherian regular local ring of mixed characteristic and dimension four, and let $r$ be a member of a regular system of parameters. We prove that every finitely generated projective module over $R[1/r]$ is free. We also prove that $\\mathrm{Sp}_4(R[1/r])$ acts transitively on unimodular columns of length four and that every determinant orientation of a rank-two projective module is induced by a basis. The argument reduces freeness to two vanishing results: the degree-three Zariski cohomology of the naive degree-four Milnor--Witt sheaf and the alternating Witt group of $R[1/r]$.…","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"ai_models":["ChatGPT"],"discussed":0,"published":"2026-10-20","reactions":{},"withdrawn":false,"authorship":"no-human-author-claimed","formalized":false,"human_understanding":"none"}