Cycles, transfers, and motivic homology theories. (English) Zbl 1021.14006

Voevodsky, Vladimir; Suslin, Andrei; Friedlander, Eric M.

Annals of Mathematics Studies. 143. Princeton, NJ: Princeton University Press. v, 254 p. (2000).

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This volume consists of six separate papers which are devoted to motivic cohomology theory and the allied theory of algebraic cycles. The authors’ original goal, which finally led to this volume, was to establish the construction of a certain “motivic cohomology theory”, whose existence was conjectured by A. Beilinson (1987) and S. Lichtenbaum (1990). However, as their motivation evolved into a quest for a deeper understanding of various properties of algebraic cycles, some of the papers presented here do not deal directly with motivic cohomology but rather with topics on algebraic cycles, Chow sheaves, higher Chow groups, and étale cohomology.
The six papers are reviewed individually (see Zbl 1019.14008; Zbl 1019.14004; Zbl 1019.14010; Zbl 1019.14011; Zbl 1019.14009; Zbl 1019.14001).

Reviewer: Werner Kleinert (Berlin)

MSC:

14F42	Motivic cohomology; motivic homotopy theory
14-02	Research exposition (monographs, survey articles) pertaining to algebraic geometry
14C25	Algebraic cycles
14C35	Applications of methods of algebraic \(K\)-theory in algebraic geometry

Keywords:

cycles; transfers; motivic homology theories