On the Lichtenbaum-Quillen Conjecture

Part of the NATO ASI Series book series (ASIC, volume 407)


The Lichtenbaum-Quillen conjecture, relating the algebraic K-theory of rings of integers in number fields to their étale cohomology, has been one of the main factors of development of algebraic K-theory in the beginning of the 1980s. Soule’ and Dwyer-Friedlander mapped algebraic K-theory of a ring of integers to its -adic cohomology by means of a ‘Chern character’, that they proved surjective. Here, on the contrary, we map étale cohomology to algebraic K-theory, providing a right inverse to these Chern characters. This gives a different proof of surjectivity, which avoids Dwyer-Friedlander’s use of ‘secondary transfer’. The constructions and results of this paper concern a much wider class of rings than rings of integers in number fields.


Exact Sequence Spectral Sequence Number Field Residue Field Chern Character 
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© Springer Science+Business Media Dordrecht 1993

Authors and Affiliations

  1. 1.CNRS — URA 212 MathématiquesUniversité de Paris 7Paris Cedex 05France

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