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arXiv · 1504.08185

On additive higher Chow groups of affine schemes

Amalendu Krishna·Jinhyun Park
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Abstract

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 \'etale descent for multivariate additive higher Chow groups.

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Amalendu Krishna, Jinhyun Park. 2015-04-30. On additive higher Chow groups of affine schemes. https://arxiv.org/abs/1504.08185

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