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On the Lichtenbaum-Quillen Conjecture

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

Abstract

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.

Keywords

Exact Sequence Spectral Sequence Number Field Residue Field Chern Character 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media Dordrecht 1993

Authors and Affiliations

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

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