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, local copy: [pdf].

This is by far my most cited paper as single author. Once I got the following comment:

If one actually reads your paper, it is very interesting.

I was using the content of the paper since 1987, mainly to compute Chow groups of some quadrics. Particular applications were considerations for K4/2 (never published) and computations for the now so-called "Rost motive" (Some new results on the Chow groups of quadrics). The first version (handwritten) stems from 1993.

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:

Related II:

Correction II:

As pointed out in the article by Ivorra (footnote on p. 171), the signs in (14.3), (14.4) are incorrect: The sign exponent n has to be replaced by n+p. (The proof "immediate from the definitions" is correct…)


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