The spectral sequence relating algebraic K-theory to motivic cohomology

By Eric Friedlander, A. Suslin. 2002

170 citations recorded by the source corpus.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/ac922b9ed15f00647fd89a8eae44028c2794352a

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Citations in the corpus

Algebraic K-Theory of Rings of Integers in Local and Global Fields (2005, unknown): “If X is any scheme, smooth overZ[1|2], the multiplicative pairing of v4 1 (see [16,32]) with the spectral sequence converging to K∗(X;Z|2) gives a morphism of spectral sequences E p,q r → E r from (5.”
On Voevodsky's algebraic K-theory spectrum BGL (2007, methodology): “ructure on the Thomason-Trobaugh K-theory [TT]. 3 1.2 A construction of BGL Let S be a regular scheme. For every S-scheme X consider the category Big(X) of big vector bundles over X (see for instance [FS] for the deﬁnition and basic properties). The assignments X →Big(X) and (f: Y →X) →f∗ : Big(X) →”
Localization theorems in topological Hochschild homology and topological cyclic homology (2008, background): “Recent work of Levine [24] axiomatizes the role of localization and Mayer-Vietoris theorems in the construction of the motivic spectral sequence [1, 14], and such theorems for TR should provide key input to the construction of this conjectural “additive” motivic spectral sequence.”
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.”
Motivic cohomology with Z/2-coefficients (2003, methodology): “Their construction was reformulated in much more natural terms and extended to all smooth varieties over fields in [ 6 ].”
RELATIVE CYCLES WITH MODULI AND REGULATOR MAPS (2014, background): “Bloch’s apparently näıve definition of higher Chow groups, given in terms of algebraic cycles, provides the right answer, as established in [21] and [38].”
On motivic cohomology with Z/l -coefficients (2008, methodology): “Their construction was reformulated in much more natural terms and extended to all smooth varieties over fields in [ 6 ].”