Homology, Homotopy and Applications

Volume 9 (2007)

Number 2

A few localisation theorems

Pages: 137 – 161

DOI: https://dx.doi.org/10.4310/HHA.2007.v9.n2.a5

Authors

Bruno Kahn (Institut de Mathématiques de Jussieu, Paris, France)

R. Sujatha (Tata Institute of Fundamental Research, Mumbai, India)

Abstract

Given a functor $T\colon \mathcal{C} \to \mathcal{D}$ carrying a class of morphisms $S \subset \mathcal{C}$ into a class $S' \subset \mathcal{D}$, we give sufficient conditions for $T$ to induce an equivalence on the localised categories. These conditions are in the spirit of Quillen’s Theorem A. We give some applications in algebraic and birational geometry.

Keywords

Gabriel-Zisman localisation, Quillen's theorem A, algebraic geometry, birational geometry

2010 Mathematics Subject Classification

14A15, 14E05, 18Axx, 18F05

Published 1 January 2007