Chow groups with coefficients

by Markus Rost (75 pages)

Doc. Math. 1 (1996), No. 16, 319-393.

MR 1418952, Zbl 864.14002.

Summary: We develop a generalization of the classical Chow groups in order to have available some standard properties for homology theories: long exact sequences, spectral sequences for fibrations, homotopy invariance and intersections. The basis for our constructions is Milnor's K-theory.

Full text: EuDML, EMIS, eLibM, local copy: [pdf].

Correction:

On page 377 there is the erroneous remark: "The flatness [of the double deformation cone] over A² (not needed in the following) may be deduced from Remark 10.1.". However, flatness does not hold in general (there is a simple example in the non-regular case). The remark is not used anywhere in the text.

Thanks to Merkurjev for pointing out the error.

Related:

• Wittringhomologie, Manfred Schmid, Dissertation, Universität Regensburg, 1998.
• The Rost-Schmid Complex of a Strongly A¹-Invariant Sheaf in: Fabien Morel, A¹-Algebraic Topology over a Field, Lecture Notes in Mathematics 2052 (2012). MR 2934577, Zbl 1263.14003.

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