Abstract
In this chapter we prove a localization theorem of Quillen for singular varieties, and a generalization of it due to Levine. These are then used to prove the so-called “Fundamental Theorem” (9.8), which computes K i (A[t, t −1]), and to relate the study of 0-cycles on normal surfaces to modules of finite length and finite projective dimension over the local rings at singular points. We begin with Quillen’s localization theorem, proved in Higher Algebraic K-Theory II.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 1996 Springer Science+Business Media New York
About this chapter
Cite this chapter
Srinivas, V. (1996). Localization for Singular Varieties. In: Algebraic K-Theory. Modern Birkhauser Classics. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-0-8176-4739-1_9
Download citation
DOI: https://doi.org/10.1007/978-0-8176-4739-1_9
Publisher Name: Birkhäuser, Boston, MA
Print ISBN: 978-0-8176-4736-0
Online ISBN: 978-0-8176-4739-1
eBook Packages: Springer Book Archive