Title: Infinite Cohen-Macaulay Posets and Non-Noetherian Stanley-Reisner Rings
Abstract: In the mid-seventies Hochster and Reisner related the algebraic and topological notions of Cohen-Macaulay rings and posets using the Stanley-Reisner ring. Reisner proved that for finite simplicial complexes, topologically Cohen-Macaulay is equivalent to the Stanley-Reisner ring being algebraically Cohen-Macaulay. Unfortunately, this idea only works for finite simplicial complexes because if the complex is infinite, the ring is no longer Noetherian, and the nice Cohen-Macaulay properties do not hold true in the non-Noetherian setting. Using local cohomology we will give a natural definition for Cohen-Macaulay modules over non-Noetherian rings and show that topologically Cohen-Macaulay is equivalent to algebraically Cohen-Macaulay for infinite yet finite dimensional simplicial complexes.