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2021 On the $K$–theory of coordinate axes in affine space
Martin Speirs
Algebr. Geom. Topol. 21(1): 137-171 (2021). DOI: 10.2140/agt.2021.21.137

Abstract

Let k be a perfect field of characteristic p>0, let Ad be the coordinate ring of the coordinate axes in affine d–space over k, and let Id be the ideal defining the origin. We evaluate the relative K–groups Kq(Ad,Id) in terms of p–typical Witt vectors of k. When d=2 the result is due to Hesselholt, and for K2 it is due to Dennis and Krusemeyer. We also compute the groups Kq(Ad,Id) in the case where k is an ind-smooth algebra over the rationals, the result being expressed in terms of algebraic de Rham forms. When k is a field of characteristic zero this calculation is due to Geller, Reid and Weibel.

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Martin Speirs. "On the $K$–theory of coordinate axes in affine space." Algebr. Geom. Topol. 21 (1) 137 - 171, 2021. https://doi.org/10.2140/agt.2021.21.137

Information

Received: 15 April 2019; Revised: 27 May 2020; Accepted: 15 June 2020; Published: 2021
First available in Project Euclid: 16 March 2021

Digital Object Identifier: 10.2140/agt.2021.21.137

Subjects:
Primary: 19D55
Secondary: 16E40

Keywords: algebraic $K$–theory , coordinate axes , cyclotomic spectra , topological cyclic homology , topological Hochschild homology

Rights: Copyright © 2021 Mathematical Sciences Publishers

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Vol.21 • No. 1 • 2021
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