On the algebraic K-theory of truncated polynomial algebras in several variables
| dc.contributor.author | Angeltveit, Vigleik | |
| dc.contributor.author | Gerhardt, Teena | |
| dc.contributor.author | Hill, Michael A. | |
| dc.contributor.author | Lindenstrauss, Ayelet | |
| dc.date.accessioned | 2014-05-28T01:31:48Z | |
| dc.date.issued | 2014-02 | |
| dc.date.updated | 2015-12-10T11:26:43Z | |
| dc.description.abstract | 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 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.sponsorship | The 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. | en_AU |
| dc.format | 25 pages | |
| dc.identifier.issn | 1865-2433 | |
| dc.identifier.uri | http://hdl.handle.net/1885/11721 | |
| dc.publisher | Cambridge University Press | |
| dc.relation | http://purl.org/au-research/grants/arc/s4801019 | |
| 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.source | Journal of K-Theory 13.4 (2014): 57-81 | |
| dc.subject | algebraic | |
| dc.subject | K-theory | |
| dc.subject | trace | |
| dc.subject | map | |
| dc.subject | truncated | |
| dc.subject | polynomial | |
| dc.subject | algebra | |
| dc.title | On the algebraic K-theory of truncated polynomial algebras in several variables | |
| dc.type | Journal article | |
| local.bibliographicCitation.issue | 1 | |
| local.bibliographicCitation.lastpage | 81 | |
| local.bibliographicCitation.startpage | 57 | |
| local.contributor.affiliation | Angeltveit, Vigleik, Australian National University | |
| local.contributor.authoremail | vigleik.angeltveit@anu.edu.au | en_AU |
| local.contributor.authoruid | u4868612) | en_AU |
| local.description.embargo | Embargo: 2015-02-28 | |
| local.identifier.absfor | 010103 - Category Theory, K Theory, Homological Algebra | |
| local.identifier.absseo | 970101 - Expanding Knowledge in the Mathematical Sciences | |
| local.identifier.ariespublication | U3488905xPUB1963 | |
| local.identifier.citationvolume | 13 | |
| local.identifier.doi | 10.1017/is013010011jkt243 | |
| local.identifier.scopusID | 2-s2.0-84894465978 | |
| local.identifier.thomsonID | 000337081300003 | |
| local.identifier.uidSubmittedBy | u4868612 | en_AU |
| local.publisher.url | http://www.cambridge.org | en_AU |
| local.type.status | Published Version | en_AU |