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The Local Cohomology of FI-modules

Banff International Research Station for Mathematical Innovation and Discovery

Much of the work in homological invariants of FI-modules has been concerned with properties of certain right exact functors. One reason for this is that the category of finitely generated FI-modules over a Noetherian ring very rarely has sufficiently many injectives. In this talk we consider the (left exact) torsion functor on the category of finitely generated FI-modules, and show that its derived functors exist. Properties of these derived functors, which we call the local cohomology functors, can be used in reproving well known theorems relating to the depth, regularity, and stable range of a module. We will also see that various facts from the local cohomology of modules over a polynomial ring have analogs in our context. This is joint work with Liping Li.

Mathematics; Commutative rings and algebras; Category theory; homological algebra; Commutative algebra

video/mp4

Author affiliation: University of Wisconsin Madison

2016-10-07

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/59395

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/4.0/