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Additive Chow groups with higher modulus and the generalized de Rham-Witt complex | Kay Ruelling
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11 Mar 2005 | Subject: | Algebraic Geometry MSC-class: 14C15 | math.AG | Abstract: | Bloch and Esnault defined additive higher Chow groups with modulus (m+1) on the level of zero cycles over a field k, denoted by TH^n(k,n;m), n,m >0. They prove that TH^n(k,n;1) is isomorphic to the group of absolute Kaehler differentials of degree n-1 over k. In this paper we generalize their result and show that TH^n(k,n;m) is isomorphic to W_mOmega^{n-1}_k, the group of degree n-1 elements in the generalized de Rham-Witt of length m over k. This complex was defined by Hesselholt and Madsen and generalizes the p-typical de Rham-Witt complex of Bloch-Deligne-Illusie. Before we can prove this theorem we have to generalize some classical results to the de Rham-Witt complex. We give a construction of the generalized de Rham-Witt complex for bmath{Z}_(p)-algebras analogous to the construction in the p-typical case. We construct a trace for finite field extensions L / k and if K is the function field of a smooth projective curve C over k and P in C is a point we define a residue map Res_P: W_mOmega^1_K --> W_m(k), which satisfies a "sum-of-residues-equal-zero" theorem. | Source: | arXiv, math.AG/0503214 | Services: | Forum | Review | PDF | Favorites |
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