Motivic Eilenberg-MacLane spaces

By Vladimir Voevodsky. 2008

103 citations recorded by the source corpus.

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.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/9c0fafb8c8fc692db78498d30f75b77b7b2aea0d

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In Geometry and Topology

In Mathematical Physics

Citations in the corpus

A comparison of motivic and classical stable homotopy theories (2011, methodology): “This follows Voevodsky’s constructions in [39], but we use a less sophisticated approach, in that we do not consider any model category structures or use derived functors.”
On motivic cohomology with Z/l -coefficients (2008, methodology): “Our proof of this theorem is inspired by [1] and uses a uniqueness argument based on the computations of [11].”
Cohomological Hasse principle and motivic cohomology for arithmetic schemes (2010, methodology): “tible on X, and deduce the vanishing of Z/ℓmZ-coeﬃcient by using the Bloch-Kato conjecture (see Section 7) recently established by Rost and Voevodsky (the whole proof is available in the papers [V1], [V2], [SJ], [HW]). We give few words on the known results on the Kato conjectures (see [Sa3, Section”
The norm residue isomorphism theorem (2009, methodology): “I am greatly indebted to Voevodsky for numerous discussions about this work, and about [ 30 ].”
The motive of a classifying space (2014, methodology): “as computing the motivic cohomology of the symmetric groups over any field [61, section 6], [62].”