Motivic cohomology groups are isomorphic to higher chow groups in any characteristic

By Vladimir Voevodsky. 2002

194 citations recorded by the source corpus.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/b59453ae08d91302eb9cd63952d3aca8a6ca8c70

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Geometry and Topology

1. Markus Spitzweck
2. P. Ostvaer
3. M. Levine
4. Thomas H. Geisser
5. S. Saito
6. Vladimir Voevodsky
7. Joël Riou
8. O. Rondigs

In Mathematical Physics

1. Markus Spitzweck
2. P. Ostvaer
3. M. Levine
4. Thomas H. Geisser
5. S. Saito
6. Joël Riou
7. Vladimir Voevodsky
8. F. Binda

Citations in the corpus

• Reduced power operations in motivic cohomology (2001, background): “The main theorem of [14] implies the following result.”
• Cancellation theorem (2002, unknown): “For K ′ being the motivic complex Z ( n )[ m ] and any field k it was proved in [5].”
• Duality via cycle complexes (2006, methodology): “ometimes omit the t when we use the Zariski topology, and note that for X over a field or discrete valuation ring [2], [26] CHn(X,i−2n)congHi(X Zar,Zc(n)). If ZX(n) is the motivic complex of Voevodsky [46], then on a smooth scheme X of dimension d over a field k, Duality via cycle complexes 5 Zc X(n) ”
• Motivic cohomology with Z/2-coefficients (2003, methodology): “8 and using [41] to identify motivic cohomology of [6] with the motivic cohomology of this paper we obtain the following results.”
• Noncommutative Geometry, Quantum Fields and Motives (2007, unknown): “[22], [315]).”
• Algebraic K‐theory, A1‐homotopy and Riemann–Roch theorems (2009, background): “The comparison with (higher) Chow groups [46] implies that, for any n 0, there is a canonical isomorphism π0K(Z(n), 2n) CH(−) in Sm/kAb, where CH(−) is the presheaf X → CH(X).”
• RELATIVE CYCLES WITH MODULI AND REGULATOR MAPS (2014, background): “omology groups have been defined by V.Voevodsky [41] and M.Levine [31] as Zariski hypercohomology of certain complexes of sheaves, and they are known to agree with Bloch’s definition in the smooth case [42]. So, if Xis any scheme of finite type over k, we are now able to consider the motivic cohomology”
• Motivic Landweber exactness (2008, background): “Recall that for smooth schemes over fields motivic cohomology coincides with higher Chow groups [40].”
• The homotopy coniveau tower (2005, methodology): “The natural setting for the homotopy coniveau tower is in the Morel–Voevodsky homotopy category of S1-spectra, SHS 1 (k).”
• An additive version of higher Chow groups (2001, unknown): “is known to give motivic cohomology [9].”