Homological Invariants of FI-modules and FI_G-modules

2015/11/12 by Ramos, Eric
#Algebraic Topology (math.AT) #Combinatorics (math.CO) #FOS: Mathematics #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.1511.03964

Abstract

We explore a theory of depth for FI_G-modules which are presented in finite degrees. Using this theory, we prove results about the regularity, and provide novel bounds on stable ranges of FI-modules, making effective a theorem of Nagpal and thereby refining the stable range in results of Church, Ellenberg, and Farb.

Related

• Depth and the Local Cohomology of FI_G-modules
• Upper bounds of homological invariants of FI_G-modules
• Bounding the homology of FI-modules
• A remark on FI-module homology
• A long exact sequence for homology of FI-modules