Homology, Homotopy and Applications

Volume 17 (2015)

Number 1

Algebraic proofs of some fundamental theorems in algebraic $K$-theory

Pages: 267 – 280

DOI: http://dx.doi.org/10.4310/HHA.2015.v17.n1.a13

Author

Tom Harris (Mathematical Sciences, University of Southampton, United Kingdom)

Abstract

We present new proofs of the additivity, resolution, and cofinality theorems for the algebraic $K$-theory of exact categories. These proofs are entirely algebraic, based on Grayson’s presentation of higher algebraic $K$-groups via binary complexes.

Keywords

higher algebraic $K$-group, acyclic binary complex, additivity theorem, resolution theorem, cofinality theorem

2010 Mathematics Subject Classification

19D99

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Published 18 May 2015