The small Cohen–Macaulay conjecture

A small Cohen–Macaulay module over a local ring is a finitely generated module whose depth equals the dimension of the ring. The small Cohen–Macaulay conjecture. Every complete local domain has a small Cohen–Macaulay module. The conjecture asks for the existence of finitely generated maximal Cohen–Macaulay modules over complete local domains; the paper discusses a new instance of this existence problem and a theorem establishing such a module under additional quasi-Gorenstein hypotheses.