Upper bounds of homological invariants of $F{I}_G$-modules

Abstract

In this paper we use a homological approach to obtain upper bounds for a few homological invariants of $F{I}_G$-modules $V$. These upper bounds are expressed in terms of the generating degree and torsion degree, which measure the top and socle of $V$ under actions of non-invertible morphisms in the category respectively.

A few small changes to make the paper more friendly to the reader

References in corpus (3)

• FI-modules and the cohomology of modular representations of symmetric groups
• Homological Invariants of FI-modules and FI_G-modules
• Filtrations and Homological degrees of FI-modules

Cited by in corpus (12)

• Central stability for the homology of congruence subgroups and the second homology of Torelli groups
• A long exact sequence for homology of FI-modules
• Periodicity in the cohomology of symmetric groups via divided powers
• Depth and the Local Cohomology of FI_G-modules
• On the degree-wise coherence of FI_G-modules
• Bounding the homology of FI-modules
• Linear stable range for homology of congruence subgroups via FI-modules
• FI${}^m$-modules over Noetherian rings
• Two homological proofs of the Noetherianity of $F{I}_G$
• Bounds on homological invariants of VI-modules
• Asymptotic behaviors of representations of graded categories with inductive functors
• An inductive machinery for representations of categories with shift functors