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 $\not = 2$ form a differential graded module over the big de Rham-Witt complex $\W_m\Omega^\bullet_R$. 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 descent for multivariate additive higher Chow groups.

2010 Mathematics Subject Classification: Primary 14C25; Secondary 13F35, 19E15

Keywords and Phrases: algebraic cycle, additive higher Chow group, Witt vectors, de Rham-Witt complex

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