Additive higher Chow groups of schemes

作者：Krishna Amalendu^*; Levine Marc

来源：Journal fur die Reine und Angewandte Mathematik, 2008, 619: 75-140.

DOI：10.1515/CRELLE.2008.041

We show how to make the additive Chow groups of Bloch-Esnault, Rulling and Park into a graded module for Bloch's higher Chow groups, in the case of a smooth projective variety over a field. This yields a projective bundle formula as well as a blow-up formula for the additive Chow groups of a smooth projective variety.
In case the base field k admits resolution of singularities, these properties allow us to apply the technique of Guillen and Navarro Aznar to de. ne the additive Chow groups ``with log poles at infinity'' for an arbitrary finite-type k-scheme X. This theory has all the usual properties of a Borel-Moore theory on finite type k-schemes: it is covariantly functorial for projective morphisms, contravariantly functorial for morphisms of smooth schemes, and has a projective bundle formula, homotopy property, and Mayer-Vietoris and localization sequences.
Finally, we show that the regulator map defined by Park from the additive Chow groups of 1-cycles to the modules of absolute Kahler differentials of an algebraically closed field of characteristic zero is surjective, giving evidence of a conjectured isomorphism between these two groups.

• 出版日期2008-6
• 单位东北大学