Localisation for Singular Varieties
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 Ki(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”.
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