On the algebraic Ktheory of truncated polynomial algebras in several variables

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Angeltveit, Vigleik; Gerhardt, Teena; Hill, Michael A.; Lindenstrauss, Ayelet
Description
We consider the algebraic Ktheory 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 Ktheory 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 Kgroups explicitly. We also compute the Kgroups modulo torsion for k = ℤ. To...[Show more]
dc.contributor.author  Angeltveit, Vigleik  

dc.contributor.author  Gerhardt, Teena  
dc.contributor.author  Hill, Michael A.  
dc.contributor.author  Lindenstrauss, Ayelet  
dc.date.accessioned  20140528T01:31:48Z  
dc.identifier.issn  18652433  
dc.identifier.uri  http://hdl.handle.net/1885/11721  
dc.description.abstract  We consider the algebraic Ktheory 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 Ktheory 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 Kgroups explicitly. We also compute the Kgroups modulo torsion for k = ℤ. To understand this Ktheory 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 ncube of spectra, each of which is easier to understand.  
dc.description.sponsorship  The first author was supported by an NSF AllInstitutes Postdoctoral Fellowship administered by the Mathematical Sciences Research Institute through its core grant DMS0441170, by NSF grant DMS0805917, 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 FA95500710555, and the Sloan Foundation.  
dc.format  25 pages  
dc.publisher  Cambridge University Press  
dc.rights  © Cambridge University Press 2014 ©2013 ISOPP http://www.sherpa.ac.uk/romeo/issn/18652433/ Author can archive preprint (ie prerefereeing); author can archive postprint (ie final draft postrefereeing); subject to 12mth embargo, publishers version/PDF may be used in an institutional repository.  
dc.source  Journal of KTheory 13.4 (2014): 5781  
dc.subject  algebraic  
dc.subject  Ktheory  
dc.subject  trace  
dc.subject  map  
dc.subject  truncated  
dc.subject  polynomial  
dc.subject  algebra  
dc.title  On the algebraic Ktheory of truncated polynomial algebras in several variables  
dc.type  Journal article  
local.identifier.citationvolume  13  
dc.date.issued  201402  
local.identifier.absfor  010103  Category Theory, K Theory, Homological Algebra  
local.identifier.ariespublication  U3488905xPUB1963  
local.publisher.url  http://www.cambridge.org  
local.type.status  Published Version  
local.contributor.affiliation  Angeltveit, Vigleik, Australian National University  
local.description.embargo  Embargo: 20150228  
dc.relation  http://purl.org/auresearch/grants/arc/s4801019  
local.bibliographicCitation.issue  1  
local.bibliographicCitation.startpage  57  
local.bibliographicCitation.lastpage  81  
local.identifier.doi  10.1017/is013010011jkt243  
local.identifier.absseo  970101  Expanding Knowledge in the Mathematical Sciences  
dc.date.updated  20151210T11:26:43Z  
local.identifier.scopusID  2s2.084894465978  
local.identifier.thomsonID  000337081300003  
Collections  ANU Research Publications 
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