Angeltveit, VigleikGerhardt, TeenaHill, Michael A.Lindenstrauss, Ayelet2014-05-281865-2433http://hdl.handle.net/1885/11721We 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.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.25 pages© 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.algebraicK-theorytracemaptruncatedpolynomialalgebra2014-0210.1017/is013010011jkt2432015-12-10