Ext and local cohomology modules of face rings of simplicial posets

TL;DR

This paper generalizes homological properties of Stanley--Reisner rings from simplicial complexes to face rings of simplicial posets, using topological and combinatorial methods.

Contribution

It extends known results on homological properties from simplicial complexes to simplicial posets, broadening the theoretical framework.

Findings

Generalization of homological theorems to simplicial posets

Extension of results by Miyazaki and Gräbe

New combinatorial-topological insights into face rings

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.