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Motivic Eilenberg-MacLane spaces

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Abstract

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.

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Authors and Affiliations

  1. School of Mathematics, Institute for Advanced Study, Princeton, NJ, 08540, USA

    Vladimir Voevodsky

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  1. Vladimir Voevodsky
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Correspondence to Vladimir Voevodsky.

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Work on the earlier versions of this paper was supported by NSF grant 0403367.

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Voevodsky, V. Motivic Eilenberg-MacLane spaces. Publ.math.IHES 112, 1–99 (2010). https://doi.org/10.1007/s10240-010-0024-9

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  • DOI: https://doi.org/10.1007/s10240-010-0024-9

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