On the local quotient structure of Artin stacks

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dc.contributor.authorAlper, Jarod
dc.date.accessioned2015-12-08T22:26:55Z
dc.date.issued2010
dc.date.updated2016-06-14T09:08:09Z
dc.description.abstractWe show that near closed points with linearly reductive stabilizer, Artin stacks are formally locally quotient stacks by the stabilizer. We conjecture that the statement holds �tale locally and we provide some evidence for this conjecture. In particular, we prove that if the stabilizer of a point is linearly reductive, the stabilizer acts algebraically on a miniversal deformation space, generalizing the results of Pinkham and Rim. We provide a generalization and stack-theoretic proof of Luna�s �tale slice theorem which shows that GIT quotient stacks are �tale locally quotients stacks by the stabilizer.
dc.identifier.issn0022-4049
dc.identifier.urihttp://hdl.handle.net/1885/33843
dc.publisherElsevier
dc.sourceJournal of Pure and Applied Algebra
dc.titleOn the local quotient structure of Artin stacks
dc.typeJournal article
local.bibliographicCitation.issue9
local.bibliographicCitation.lastpage1591
local.bibliographicCitation.startpage1576
local.contributor.affiliationAlper, Jarod, College of Physical and Mathematical Sciences, ANU
local.contributor.authoremailu5266438@anu.edu.au
local.contributor.authoruidAlper, Jarod, u5266438
local.description.embargo2037-12-31
local.description.notesImported from ARIES
local.identifier.absfor010102 - Algebraic and Differential Geometry
local.identifier.absseo970101 - Expanding Knowledge in the Mathematical Sciences
local.identifier.ariespublicationu4743872xPUB106
local.identifier.citationvolume214
local.identifier.doi10.1016/j.jpaa.2009.11.016
local.identifier.scopusID2-s2.0-76149094138
local.identifier.thomsonID000275517700006
local.identifier.uidSubmittedByu4743872
local.type.statusPublished Version

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