Two homological proofs of the Noetherianity of $F{I}_G$

Abstract

We give two homological proofs of the Noetherianity of the category $FI$, a fundamental result discovered by Church, Ellenberg, Farb, and Nagpal.

Proofs of certain main results are simplified using a key proposition notified to the author by Ramos

References in corpus (6)

• FI-modules and the cohomology of modular representations of symmetric groups
• Homological Invariants of FI-modules and FI_G-modules
• A long exact sequence for homology of FI-modules
• Upper bounds of homological invariants of $F{I}_G$-modules
• Depth and the Local Cohomology of FI_G-modules
• Filtrations and Homological degrees of FI-modules

Cited by in corpus (4)

• On the degree-wise coherence of FI_G-modules
• ${\mathrm{FI}}_G$-modules, orbit configuration spaces, and complex reflection groups
• FI${}^m$-modules over Noetherian rings
• An inductive machinery for representations of categories with shift functors