Title	Equivariant Hilbert Series in non-Noetherian Polynomial Rings
Creator	Nagel, Uwe
Publisher	Banff International Research Station for Mathematical Innovation and Discovery
Date Issued	2016-04-08T09:59
Description	Ideals in polynomial rings in countably many variables that are invariant under a suitable action of a symmetric group or the monoid of strictly increasing functions arise in various contexts. We study such an ideal using an ascending chain of invariant ideals. We establish that the associated equivariant Hilbert series is a rational function in two variables. This is used to prove that the Krull dimensions and multiplicities of ideals in such an invariant filtration grow eventually linearly and exponentially, respectively. Furthermore, we determine the terms that dominate this growth. This may also be viewed as a method for assigning new asymptotic invariants to a homogenous ideal in a noetherian polynomial ring. This is based on joint work with Tim Roemer.
Extent	60 minutes
Subject	Mathematics; Commutative rings and algebras; Category theory; homological algebra; Commutative algebra
Type	Moving Image
File Format	video/mp4
Language	eng
Notes	Author affiliation: University of Kentucky
Series	BIRS Workshop Lecture Videos (Banff, Alta)
Date Available	2016-10-08
Provider	Vancouver : University of British Columbia Library
Rights	Attribution-NonCommercial-NoDerivatives 4.0 International
DOI	10.14288/1.0319072
URI	http://hdl.handle.net/2429/59408
Affiliation	Non UBC
Peer Review Status	Unreviewed
Scholarly Level	Faculty
Rights URI	http://creativecommons.org/licenses/by-nc-nd/4.0/
Aggregated Source Repository	DSpace

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Equivariant Hilbert Series in non-Noetherian Polynomial Rings Nagel, Uwe

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