Hostname: page-component-586b7cd67f-dsjbd Total loading time: 0 Render date: 2024-11-28T17:14:59.089Z Has data issue: false hasContentIssue false
  • English
  • Français

K-theory for ring C*-algebras attached to function fields with only one infinite place

Published online by Cambridge University Press:  31 January 2012

Xin Li
Xin Li*
Affiliation:
Mathematisches Institut, Einsteinstrasse 62, 48149 Münster, [email protected]
Get access

Abstract

We study the K-theory of ring C*-algebras associated to rings of integers in global function fields with only a single infinite place. First, we compute the torsion-free part of the K-groups of these ring C*-algebras. Secondly, we show that, under a certain primeness condition, the torsion part of K-theory determines the inertia degrees at infinity of our function fields.

Keywords

K-theoryring C*-algebrafunction field
Type
Research Article
Information
Journal of K-Theory , Volume 10 , Issue 1 , August 2012 , pp. 203 - 231
Copyright
Copyright © ISOPP 2011

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Cun.Cuntz, J., C*-algebras associated with the ax + b-semigroup over ℕ (English), Cortiñas, Guillermo et al. (ed.), K-theory and noncommutative geometry. Proceedings of the ICM 2006 satellite conference, Valladolid, Spain, August 31-September 6, 2006. Zürich: Euro. Math. Soc. (EMS). Series of Congress Reports, 201–215 (2008).Google Scholar
Cu-Li1.Cuntz, J. and Li, X., The regular C*-algebra of an integral domain, in Quanta of Maths, Clay Math. Proc. 11, Amer. Math. Soc., Providence, RI, 2010, 149–170.Google Scholar
Cu-Li2.Cuntz, J. and Li, X., C*-algebras associated with integral domains and crossed products by actions on adele spaces, Journal of Noncommutative Geometry 5 (2011), 1–37.Google Scholar
Cu-Li3.Cuntz, J. and Li, X., K-theory for ring C*-algebras attached to polynomial rings over finite fields, Journal of Noncommutative Geometry 5 (2011), 331–349.Google Scholar
Hi-Ro.Higson, N. and Roe, J., Analytic K-Homology, Oxford University Press, New York, 2000.Google Scholar
Li.Li, X., Ring C*-algebras, Math. Ann. 348 (2010), 859–898.Google Scholar
Neu.Neukirch, J., Algebraic number theory, Die Grundlehren der mathematischen Wissenschaften, Springer-Verlag, Berlin, 1999.Google Scholar
P-V.Pimsner, M. and Voiculescu, D., Exact sequences for K-groups and Ext-groups of certain cross-product C*-algebras, J. Operator Theory 4 (1980), 93–118.Google Scholar
Ro.Rosen, M., Number theory in function fields, Springer-Verlag, New York, 2002.Google Scholar
Weil.Weil, A., Basic number theory, Reprint of the 1974 Edition, Springer-Verlag, Berlin Heidelberg New York, 1995.Google Scholar