Bloch-Kato Conjecture and Motivic Cohomology with Finite Coefficients

By A. Suslin, Vladimir Voevodsky. 2000

346 citations recorded by the source corpus.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/4cdcac2473ee2d7d2785820c38541947cf806357

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Citations in the corpus

The K-theory of fields in characteristic p (2000, background): “for i ≤ n. Suslin and Voevodsky [ 27 ] show that, assuming resolution of singularities, the Bloch-Kato conjecture”
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”
Motivic cohomology groups are isomorphic to higher chow groups in any characteristic (2002, background): “In this short paper we show that the motivic cohomology groups defined in [3] are isomorphic to the motivic cohomology groups defined in [1] for smooth schemes over any field.”
Oriented Cohomology Theories of Algebraic Varieties (2003, background): “Let A be the motivic cohomology [28]: ApZ(X) = ⊕q=0H Z (X,Z(q)).”
The Bloch-Kato conjecture and a theorem of Suslin-Voevodsky (2001, methodology): “Introduction The purpose of this paper is to give an alternate proof of the main result of [19], along the lines of [10]; our proof does not rely on resolution of singularities, hence extends the results of [19] to varieties over fields of arbitrary characteristic.”
The norm residue isomorphism theorem (2009, background): “We will also be interested in the Lefschetz motives LR = Rtr(A /A − 0), which represent integral motivic cohomology in the triangulated category DM (R) of effective motives or its full subcategory DM ,− (see [9, 23, 26].”
K-regularity, cdh-fibrant Hochschild homology, and a conjecture of Vorst (2006, background): “Recall from [13] that the scdh topology on Sm/F is the restriction of the cdh topology on Sch/F .”
The smooth Whitehead spectrum of a point at odd regular primes (2003, result): “The oddprimary version of this conjecture would follow [41] from results on the Bloch{ Kato conjecture [4] announced as \in preparation" by Rost and Voevodsky, but have not yet formally appeared.”
A1-Algebraic Topology over a Field (2012, background): “We denote by Sing A1 • (F ) the space (or simplicial sheaf of sets) U 7→ F (∆• × U), and we call it the SuslinVoevodsky construction on F [83, 84].”