Motivic cohomology and higher Chow groups

1998 ◽  
pp. 53-106
Author(s):  
Marc Levine
Keyword(s):  
Chow Groups ◽  
Motivic Cohomology ◽  
Higher Chow Groups

Algebraic K-theory and higher Chow groups of linear varieties

2001 ◽  
Vol 130 (1) ◽  
pp. 37-60 ◽  
Author(s):  
ROY JOSHUA
Keyword(s):  
General Condition ◽  
Chow Groups ◽  
Closed Field ◽  
Spectral Sequences ◽  
Motivic Cohomology ◽  
Algebraically Closed Field ◽  
Arbitrary Characteristic ◽  
Base Scheme ◽  
Kunneth Formula ◽  
Higher Chow Groups

The main focus in this paper is the algebraic K-theory and higher Chow groups of linear varieties and schemes. We provide Kunneth spectral sequences for the higher algebraic K-theory of linear schemes flat over a base scheme and for the motivic cohomology of linear varieties defined over a field. The latter provides a Kunneth formula for the usual Chow groups of linear varieties originally obtained by different means by Totaro. We also obtain a general condition under which the higher cycle maps of Bloch from mod-lv higher Chow groups to mod-lv étale cohomology are isomorphisms for projective nonsingular varieties defined over an algebraically closed field of arbitrary characteristic p [ges ] 0 with l ≠ p. It is observed that the Kunneth formula for the Chow groups implies this condition for linear varieties and we compute the mod-lv motivic cohomology and mod-lv algebraic K-theory of projective nonsingular linear varieties to be free ℤ/lv-modules.

scholarly journals The Abel–Jacobi map for higher Chow groups

2006 ◽  
Vol 142 (02) ◽  
pp. 374-396 ◽  
Author(s):  
Matt Kerr ◽  
James D. Lewis ◽  
Stefan Müller-Stach
Keyword(s):  
Chow Groups ◽  
Higher Chow Groups

Polygonal cycles in higher Chow groups of Jacobians

2004 ◽  
Vol 183 (3) ◽  
pp. 387-399 ◽  
Author(s):  
J.C. Naranjo ◽  
G.P. Pirola ◽  
F. Zucconi
Keyword(s):  
Chow Groups ◽  
Higher Chow Groups

DGA-Structure on Additive Higher Chow Groups

2013 ◽  
Vol 2015 (1) ◽  
pp. 1-54 ◽  
Author(s):  
Amalendu Krishna ◽  
Jinhyun Park
Keyword(s):  
Chow Groups ◽  
Higher Chow Groups

scholarly journals Higher Chow groups of varieties with group action

2013 ◽  
Vol 7 (2) ◽  
pp. 449-506 ◽  
Author(s):  
Amalendu Krishna
Keyword(s):  
Group Action ◽  
Chow Groups ◽  
Higher Chow Groups

A CONSTRUCTION OF SURFACES WITH LARGE HIGHER CHOW GROUPS

2018 ◽  
Vol 236 ◽  
pp. 311-331
Author(s):  
TOMOHIDE TERASOMA
Keyword(s):  
Power Series ◽  
Linear Algebra ◽  
Chow Groups ◽  
Chow Group ◽  
Spectral Sequences ◽  
Configurations Of Lines ◽  
Higher Chow Group ◽  
Extension Class ◽  
Higher Chow Groups

In this paper, we construct surfaces in $\mathbf{P}^{3}$ with large higher Chow groups defined over a Laurent power series field. Explicit elements in higher Chow group are constructed using configurations of lines contained in the surfaces. To prove the independentness, we compute the extension class in the Galois cohomologies by comparing them with the classical monodromies. It is reduced to the computation of linear algebra using monodromy weight spectral sequences.

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