Ext and local cohomology modules of face rings of simplicial posets

Abstract

There are a large number of theorems detailing the homological properties of the Stanley--Reisner ring of a simplicial complex. Here we attempt to generalize some of these results to the case of a simplicial poset. By investigating the combinatorics of certain modules associated with the face ring of a simplicial poset from a topological viewpoint, we extend some results of Miyazaki and Gr\"abe to a wider setting.