Depth and the Local Cohomology of FI_G-modules

Liping Li Eric Ramos

Arithmetic Geometry and Commutative Algebra K-Theory and Homology Representation Theory Rings and Algebras mathscidoc:1702.07001

In this paper we describe a machinery for homological calculations of representations of FI_G, and use it to develop a local cohomology theory over any commutative Noetherian ring. As an application, we show that the depth introduced by the second author coincides with a more classical invariant from commutative algebra, and obtain upper bounds of a few important invariants of FI_G-modules in terms of torsion degrees of their local cohomology groups.
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  title={Depth and the Local Cohomology of FI_G-modules},
  author={Liping Li, and Eric Ramos},
Liping Li, and Eric Ramos. Depth and the Local Cohomology of FI_G-modules.
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