Additive higher Chow groups of schemes
نویسندگان
چکیده
منابع مشابه
On Additive Higher Chow Groups of Affine Schemes
We show that the multivariate additive higher Chow groups of a smooth affine k-scheme Spec (R) essentially of finite type over a perfect field k of characteristic 6= 2 form a differential graded module over the big de Rham-Witt complex WmΩ • R. In the univariate case, we show that additive higher Chow groups of Spec (R) form a Witt-complex over R. We use these structures to prove an étale desce...
متن کامل00 7 Additive Higher Chow Groups of Schemes
We show how to make the additive Chow groups of Bloch-Esnault, Rülling 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 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 admits resolution of singularieties, these propertie...
متن کاملRegulators on Additive Higher Chow Groups
As an attempt to understand motives over k[x]/(xm), we define the cubical additive higher Chow groups with modulus for all dimensions extending the works of S. Bloch, H. Esnault and K. Rülling on 0-dimensional cycles. We give an explicit construction of regulator maps on the groups of 1-cycles with an aid of the residue theory of A. Parshin and V. Lomadze.
متن کاملAn Additive Version of Higher Chow Groups Une Version Additive Des Groupes De Chow Supérieurs
The cosimplicial scheme ∆• = ∆ →∆1 → → → . . . ; ∆ n := Spec ( k[t0, . . . , tn]/( ∑ ti − t) ) was used in[3] to define higher Chow groups. In this note, we let t tend to 0 and replace ∆• by a degenerate version Q• = Q →Q1 → → → . . . ; Q n := Spec ( k[t0, . . . , tn]/( ∑ ti) ) to define an additive version of the higher Chow groups. For a field k, we show the Chow group of 0-cycles on Q in thi...
متن کاملHigher Arithmetic Chow Groups
We give a new construction of higher arithmetic Chow groups for quasi-projective arithmetic varieties over a field. Our definition agrees with the higher arithmetic Chow groups defined by Goncharov for projective arithmetic varieties over a field. These groups are the analogue, in the Arakelov context, of the higher algebraic Chow groups defined by Bloch. The degree zero group agrees with the a...
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ژورنال
عنوان ژورنال: Journal für die reine und angewandte Mathematik (Crelles Journal)
سال: 2008
ISSN: 0075-4102,1435-5345
DOI: 10.1515/crelle.2008.041