Algebraic K-theory of the infinite place

We show that the algebraic K -theory of generalized archimedean valuation rings occurring in Durov’s compactification of the spectrum of a number ring is given by stable homotopy groups of certain classifying spaces. We also show that the “residue field at infinity” is badly behaved from a K -theore...

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Veröffentlicht in:	Journal of homotopy and related structures 2015-12, Vol.10 (4), p.821-842
1. Verfasser:	Scholbach, Jakob
Format:	Artikel
Sprache:	eng
Schlagworte:	Algebra Algebraic Topology Functional Analysis Mathematics Mathematics and Statistics Number Theory
Online-Zugang:	Volltext
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Beschreibung
Zusammenfassung:	We show that the algebraic K -theory of generalized archimedean valuation rings occurring in Durov’s compactification of the spectrum of a number ring is given by stable homotopy groups of certain classifying spaces. We also show that the “residue field at infinity” is badly behaved from a K -theoretic point of view.
ISSN:	2193-8407 1512-2891
DOI:	10.1007/s40062-014-0085-4