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On the algebraic K-theory of truncated polynomial algebras in several variables

Angeltveit, Vigleik; Gerhardt, Teena; Hill, Michael A.; Lindenstrauss, Ayelet

Description

We consider the algebraic K-theory of a truncated polynomial algebra in several commuting variables, K(k[x1......xn]/(x1a1…….xnan). This naturally leads to a new generalization of the big Witt vectors. If k is a perfect field of positive characteristic we describe the K-theory computation in terms of a cube of these Witt vectors on ℕ n . If the characteristic of k does not divide any of the ai we compute the K-groups explicitly. We also compute the K-groups modulo torsion for k = ℤ. To...[Show more]

dc.contributor.authorAngeltveit, Vigleik
dc.contributor.authorGerhardt, Teena
dc.contributor.authorHill, Michael A.
dc.contributor.authorLindenstrauss, Ayelet
dc.date.accessioned2014-05-28T01:31:48Z
dc.identifier.issn1865-2433
dc.identifier.urihttp://hdl.handle.net/1885/11721
dc.description.abstractWe consider the algebraic K-theory of a truncated polynomial algebra in several commuting variables, K(k[x1......xn]/(x1a1…….xnan). This naturally leads to a new generalization of the big Witt vectors. If k is a perfect field of positive characteristic we describe the K-theory computation in terms of a cube of these Witt vectors on ℕ n . If the characteristic of k does not divide any of the ai we compute the K-groups explicitly. We also compute the K-groups modulo torsion for k = ℤ. To understand this K-theory spectrum we use the cyclotomic trace map to topological cyclic homology, and write TC(k[x1…….xn]/(x1a1……..xnan))as the iterated homotopy cofiber of an n-cube of spectra, each of which is easier to understand.
dc.description.sponsorshipThe first author was supported by an NSF All-Institutes Postdoctoral Fellowship administered by the Mathematical Sciences Research Institute through its core grant DMS-0441170, by NSF grant DMS-0805917, and by an Australian Research Council Discovery grant. The second author was supported by NSF DMS–1007083 and NSF DMS–1149408. The third author was supported by NSF DMS–0906285, DARPA FA9550-07-1-0555, and the Sloan Foundation.
dc.format25 pages
dc.publisherCambridge University Press
dc.rights© Cambridge University Press 2014 ©2013 ISOPP http://www.sherpa.ac.uk/romeo/issn/1865-2433/ Author can archive pre-print (ie pre-refereeing); author can archive post-print (ie final draft post-refereeing); subject to 12mth embargo, publishers version/PDF may be used in an institutional repository.
dc.sourceJournal of K-Theory 13.4 (2014): 57-81
dc.subjectalgebraic
dc.subjectK-theory
dc.subjecttrace
dc.subjectmap
dc.subjecttruncated
dc.subjectpolynomial
dc.subjectalgebra
dc.titleOn the algebraic K-theory of truncated polynomial algebras in several variables
dc.typeJournal article
local.identifier.citationvolume13
dc.date.issued2014-02
local.identifier.absfor010103 - Category Theory, K Theory, Homological Algebra
local.identifier.ariespublicationU3488905xPUB1963
local.publisher.urlhttp://www.cambridge.org
local.type.statusPublished Version
local.contributor.affiliationAngeltveit, Vigleik, Australian National University
local.description.embargoEmbargo: 2015-02-28
dc.relationhttp://purl.org/au-research/grants/arc/s4801019
local.bibliographicCitation.issue1
local.bibliographicCitation.startpage57
local.bibliographicCitation.lastpage81
local.identifier.doi10.1017/is013010011jkt243
local.identifier.absseo970101 - Expanding Knowledge in the Mathematical Sciences
dc.date.updated2015-12-10T11:26:43Z
local.identifier.scopusID2-s2.0-84894465978
local.identifier.thomsonID000337081300003
CollectionsANU Research Publications

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