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Excision in algebraic $K$-theory revisited

Part of: Higher algebraic $K$-theory Abelian categories

Published online by Cambridge University Press:  06 August 2018

Georg Tamme
Georg Tamme*
Affiliation:
Fakultät für Mathematik, Universität Regensburg, D-93040 Regensburg, Germany email georg.tamme@ur.de
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Abstract

By a theorem of Suslin, a Tor-unital (not necessarily unital) ring satisfies excision in algebraic $K$-theory. We give a new and direct proof of Suslin’s result based on an exact sequence of categories of perfect modules. In fact, we prove a more general descent result for a pullback square of ring spectra and any localizing invariant. Our descent theorem contains not only Suslin’s result, but also Nisnevich descent of algebraic $K$-theory for affine schemes as special cases. Moreover, the role of the Tor-unitality condition becomes very transparent.

Keywords

excisionlocalizing invariantalgebraic K-theory

MSC classification

Primary: 18E30: Derived categories, triangulated categories
Secondary: 19D99: None of the above, but in this section
Type
Research Article
Information
Compositio Mathematica , Volume 154 , Issue 9 , September 2018 , pp. 1801 - 1814
Copyright
© The Author 2018 

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Footnotes

The author is supported by the CRC 1085 Higher Invariants (Universität Regensburg) funded by the DFG.

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