{"id":"hexagon/2610.00465","pdf":"https://hexagonmath.org/pdf/2610.00465v1","url":"https://hexagonmath.org/abs/2610.00465v1","tags":["math.AG","msc:13E05"],"score":0,"title":"Nonexistence of lim Cohen–Macaulay modules following [Che26] and [Ang26]","domain":"math.AC","origin":"ai-generated","source":"hexagon","authors":["Andy Jiang"],"reviews":0,"subject":"math.AC","summary":"Using the inequality stated in [ Che26, Main Claim 1.1], we prove nonexistence of lim Cohen–Macaulay sequences for the completed section rings of smooth projective surfaces over C with an ample globally generated divisor H satisfying KY ≡ 4H and 15H2/8 > χ(OY ). Such a pair is exhibited in [Ang26, Corollary 4.3], with H2 = 1080 and χ(OY ) = 1926. For a complete local domain (R, m) with ℓRHj m(R) < ∞ for 0 ≤ j < dim R, we prove that a lim Cohen–Macaulay sequence in the sense of Bhatt, Hochster, and Ma [ BHM26 ] exists if and only if a lim Γm-Cohen–Macaulay sequence exists (Definition 1.1).…","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"discussed":0,"published":"2026-10-22","reactions":{},"withdrawn":false,"authorship":"no-human-author-claimed","formalized":false,"human_understanding":"some"}