## On additive higher Chow groups of affine schemes

### Summary

Summary: 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.

### Mathematics Subject Classification

14C25, 13F35, 19E15

### Keywords/Phrases

algebraic cycle, additive higher Chow group, Witt vectors, de Rham-Witt complex