On the algebraic K-theory of the coordinate axes over the integers

Vigleik Angeltveit; Teena Gerhardt

doi:10.4310/HHA.2011.v13.n2.a7

On the algebraic K-theory of the coordinate axes over the integers

Vigleik Angeltveit^*, Teena Gerhardt

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

2 Citations (Scopus)

Abstract

We show that the relative algebraic K-theory group K_2i(Z[x; y]=(xy); (x; y)) is free abelian of rank 1 and that K_2i+1(Z[x; y]=(xy); (x; y)) is finite of order (i!)². We also find the group structure of K_2i+1(Z[x; y]=(xy); (x; y)) in low degrees.

Original language	English
Pages (from-to)	103-111
Number of pages	9
Journal	Homology, Homotopy and Applications
Volume	13
Issue number	2
DOIs	https://doi.org/10.4310/HHA.2011.v13.n2.a7
Publication status	Published - 2011

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10.4310/HHA.2011.v13.n2.a7

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abstract = "We show that the relative algebraic K-theory group K2i(Z[x; y]=(xy); (x; y)) is free abelian of rank 1 and that K2i+1(Z[x; y]=(xy); (x; y)) is finite of order (i!)2. We also find the group structure of K2i+1(Z[x; y]=(xy); (x; y)) in low degrees.",

keywords = "Algebraic k-theory, Equivariant homotopy, Topological cyclic homology",

author = "Vigleik Angeltveit and Teena Gerhardt",

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AB - We show that the relative algebraic K-theory group K2i(Z[x; y]=(xy); (x; y)) is free abelian of rank 1 and that K2i+1(Z[x; y]=(xy); (x; y)) is finite of order (i!)2. We also find the group structure of K2i+1(Z[x; y]=(xy); (x; y)) in low degrees.

KW - Algebraic k-theory

KW - Equivariant homotopy

KW - Topological cyclic homology

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JO - Homology, Homotopy and Applications

JF - Homology, Homotopy and Applications

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On the algebraic K-theory of the coordinate axes over the integers

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