On the algebraic K-theory of truncated polynomial algebras in several variables
Date
2014-02
Authors
Angeltveit, Vigleik
Gerhardt, Teena
Hill, Michael A.
Lindenstrauss, Ayelet
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Publisher
Cambridge University Press
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.
Description
Keywords
algebraic, K-theory, trace, map, truncated, polynomial, algebra
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Source
Journal of K-Theory 13.4 (2014): 57-81
Type
Journal article
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Embargo: 2015-02-28