Chow groups with modulus are a non-homotopy invariant variant of Chow groups.
In the theory of motives one studies A^1-homotopy invariant phenomena, like higher Chow groups/motivic cohomology and homotopy invariant algebraic K-theory. It is expected that the various categories of motives can be embedded into larger ones which also contain non-homotopy invariant phenomena, like (honest) algebraic K-theory. (Higher) Chow groups with modulus are expected to play the role of higher Chow groups in these larger categories.
Kay Rülling, Takao Yamazaki?, Suslin homology of relative curves with modulus, arXiv:1505.05922.
Federico Binda, Shuji Saito?, Relative cycles with moduli and regulator maps, arXiv:1212.0385.
Moritz Kerz, Shuji Saito?, Chow group of 0-cycles with modulus and higher dimensional class field theory, arXiv:1304.4400.
Amalendu Krishna, Jinhyun Park?, A module structure and a vanishing theorem for cycles with modulus, arXiv:1412.7396.
Amalendu Krishna, 0-cycles with modulus on surfaces, arXiv:1504.03125.
Kay Rülling, Shuji Saito?, Higher Chow groups with modulus and relative Milnor K-theory, arXiv:1504.02669.
Amalendu Krishna, Jinhyun Park?, A moving lemma for cycles with very ample modulus, arXiv:1507.05429.
Wataru Kai?, A moving lemma for algebraic cycles with modulus and contravariance, arXiv:1507.07619.
Bruno Kahn, Shuji Saito?, Takao Yamakazi?, Reciprocity sheaves, I, arXiv:1402.4201.
Bruno Kahn, Reciprocity sheaves, notes from a talk in “Homotopical methods in algebraic geometry”, USC, Los Angeles, May 28 – June 1, 2013, pdf.
Florian Ivorra, Kay Rülling, K-groups of reciprocity functors, arXiv:1209.1217.
Spencer Bloch, Hélène Esnault, An additive version of higher Chow groups, arXiv:math/0112101.
Last revised on September 12, 2015 at 13:13:25. See the history of this page for a list of all contributions to it.