The Bloch-Ogus--Gabber Theorem, by Jean-Louis Colliot-Thélène, Raymond T. Hoobler, and Bruno Kahn

In this paper, we give an exposition of Gabber's proof of the Bloch-Ogus theorem for étale cohomology with locally constructible torsion coefficients. We then abstract the ingredients of the proof to give an axiomatic treatment of it. The axioms involved are much less demanding than those of Bloch and Ogus and therefore apply to a vaster array of cohomology theories. We also give a detailed treatment of universal exactness à la Grayson, as well as several applications.

This paper has appeared in Fields Institute for Research in Mathematical Sciences Communications Series 16, A.M.S., 1997, 31-94, so the dvi files have been removed. See

Jean-Louis Colliot-Thélène <>
Raymond T. Hoobler <>
Bruno Kahn <>