Moving lemma for additive higher Chow groups

Moving Lemma for Additive Chow Groups and Applications

We study additive higher Chow groups with several modulus conditions. Apart from exhibiting the validity of all known results for the additive Chow groups with these modulus conditions, we prove the moving lemma for them: for a smooth projective variety X and a finite collection W of its locally closed algebraic subsets, every additive higher Chow cycle is congruent to an admissible cycle inter...

Moving lemma for additivehigher Chow groups

Regulators 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.

An 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...

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...