Localisation for Singular Varieties

Abstract

In this chapter we prove a localisation theorem of Quillen for singular varieties, and a generalisation 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 localisation theorem, proved in “Higher Algebraic K-theory II”.