In this paper, we construct surfaces in $\mathbf{P}^{3}$ with large higher Chow groups defined over a Laurent power series field. Explicit elements in higher Chow group are constructed using configurations of lines contained in the surfaces. To prove the independentness, we compute the extension class in the Galois cohomologies by comparing them with the classical monodromies. It is reduced to the computation of linear algebra using monodromy weight spectral sequences.

中文翻译：

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具有较大的较高 Chow 群体的表面构造

在本文中，我们在$\mathbf{P}^{3}$在 Laurent 幂级数场上定义了较大的较高 Chow 组。高级 Chow 组中的显式元素是使用包含在曲面中的线配置构建的。为了证明独立性，我们通过将伽罗瓦上同调中的扩展类与经典单调进行比较来计算它们。它简化为使用单调权重谱序列计算线性代数。