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In this paper we construct symmetric powers in the motivic homotopy categories of morphisms and finite correspondences associated with f-admissible subcategories in the categories of schemes of finite type over a field. Using this construction we provide a description of the motivic Eilenberg-MacLane spaces representing motivic cohomology on some f-admissible categories including the category of semi-normal quasi-projective schemes and, over fields which admit resolution of singularities, on some admissible subcategories including the category of smooth schemes. This description is then used to give a complete computation of the algebra of bistable motivic cohomological operations on smooth schemes over fields of characteristic zero and to obtain partial results on unstable operations which are required for the proof of the Bloch-Kato conjecture.
@article{PMIHES_2010__112__1_0,
author = {Voevodsky, Vladimir},
title = {Motivic {Eilenberg-MacLane} spaces},
journal = {Publications Math\'ematiques de l'IH\'ES},
pages = {1--99},
publisher = {Springer-Verlag},
volume = {112},
year = {2010},
doi = {10.1007/s10240-010-0024-9},
mrnumber = {2737977},
zbl = {1227.14025},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.1007/s10240-010-0024-9/}
}
TY - JOUR AU - Voevodsky, Vladimir TI - Motivic Eilenberg-MacLane spaces JO - Publications Mathématiques de l'IHÉS PY - 2010 SP - 1 EP - 99 VL - 112 PB - Springer-Verlag UR - http://geodesic.mathdoc.fr/articles/10.1007/s10240-010-0024-9/ DO - 10.1007/s10240-010-0024-9 LA - en ID - PMIHES_2010__112__1_0 ER -
Voevodsky, Vladimir. Motivic Eilenberg-MacLane spaces. Publications Mathématiques de l'IHÉS, Tome 112 (2010), pp. 1-99. doi: 10.1007/s10240-010-0024-9
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