The Bloch-Kato conjecture and a theorem of Suslin-Voevodsky

By Thomas H. Geisser, M. Levine. 2001

166 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/49b5f9af689f75e1424cd3a513a68289b6048931

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In Geometry and Topology

Citations in the corpus

On motivic cohomology with Z/l -coefficients (2008, methodology): “The relation between (3) and Conjecture 1.1 for l �= char(k) was clarified in [33] and [ 8 ] where it was shown that (3), in a given weight n ,i s in fact equivalent to Conjecture 1.1 in the same weight and moreover that it is sufficient to show only the surjectivity of (4) and the injectivity follo”
Weight structures vs. $t$-structures; weight filtrations, spectral sequences, and complexes (for motives and in general) (2007, result): “We recall that this statement is equivalent to the Bloch-Kato Conjecture (see [29] and [14]).”
The Local Structure of Algebraic K-Theory (2012, methodology): “The link between the Bloch-Kato conjecture and the Beilinson-Lichtenbaum conjectures was proved by Suslin and Voevodsky assuming resolution of singularities (this condition is removed by Geisser and Levine in [95]).”
The K-theory of fields in characteristic p (2000, methodology): “In a forthcoming paper [ 10 ], we use the methods of this paper to remove the resolution of singularities hypothesis in the theorem of Suslin and Voevodsky.”
Motivic cohomology with Z/2-coefficients (2003, methodology): “The relation between (3) and Conjecture 1.1 for l � char(k) was clarified in [33] and [ 8 ] where it was shown that (3), in a given weight n ,i s in fact equivalent to Conjecture 1.1 in the same weight and moreover that it is sufficient to show only the surjectivity of (4) and the injectivity follow”
Cohomological Hasse principle and motivic cohomology for arithmetic schemes (2010, methodology): “cles, which is a consequence of higher dimensional class ﬁeld theory ([Sa1] and [CTSS]). One way to approach the problem is to look at an ´etale cycle map constructed by Bloch [B], Geisser and Levine [GL2] and Levine [Le] (see also [Ge1]): Fix an integer n > 0. Let CHr(X,q;Z/nZ) be the higher Cho”