On motivic cohomology with Z/l -coefficients

By Vladimir Voevodsky. 2008

429 citations recorded by the source corpus.

In this paper we prove the conjecture of Bloch and Kato which relates Milnor’s K-theory of a field with its Galois cohomology as well as the related comparisons results for motivic cohomology with finite coefficients in the Nisnevich and etale topologies.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/ab0b2bd6f239aa9cfa914a6dea0d74f40dd1c452

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Citations in the corpus

A commutative P^1-spectrum representing motivic cohomology over Dedekind domains (2012, positive): “] (which we can apply since the Bloch-Kato conjecture is proven, [44]) we have MX(r) ≅ τ≤(r+1)Rǫ∗Mét(r).”
Galois equivariance and stable motivic homotopy theory (2014, methodology): “Its study was initiated by Morel and Voevodsky [40] in work related to Rost and Voevodsky’s resolution of the Bloch-Kato conjectures on Milnor K-theory and Galois cohomology [49, 52].”
The norm residue isomorphism theorem (2009, methodology): “The point of [30], and of this paper, is that S −1(A) is a Rost motive in the sense of Definition 1.”
The Local Structure of Algebraic K-Theory (2012, background): “Eventually this is now a theorem, the norm residue isomorphism theorem, due to Rost and Voevodsky, see [303], [294].”
Chow Rings, Decomposition of the Diagonal, and the Topology of Families (2014, background): “This result, also proved in [6], is a consequence of the Bloch–Kato conjecture, which has now been proved by Voevodsky and Rost.”
Motivic Eilenberg-MacLane spaces (2008, background): “Weibel in [36] and plays an important role in one of the key arguments of [32].”
On standard norm varieties (2012, background): “The existence statement is proved in [35] and [30].”
Abel-Jacobi map, integral Hodge classes and decomposition of the diagonal (2010, methodology): “The following result is proved in [7], using the Bloch-Kato conjecture recently proved by Voevodsky [27]: There is an exact sequence for any n : where the notation [ n ] means that we take the n -torsion.”
Quotients of absolute Galois groups which determine the entire Galois cohomology (2009, methodology): “The conjecture was proved for r = 2 by Merkurjev and Suslin [MS82], for r arbitrary and m = 2 by Voevodsky [ Voe03a ], and in general by Rost, Voevodsky, with a patch by Weibel ([Voe03b], [Wei09], [Wei08], [HW09]).”