摘要翻译：
证明了数域的余维2上的Bloch积分立方高阶Chow复形中分数次线性圈之间的关系，这些关系对应于对数函数方程。正如我们将用几个例子证明的那样，这些关系足以在Bloch积分高周群CH^2(F，3)中写下足够多的关系，用于检测一定数目的场F的扭转循环。利用调节器映射对上同调进行去木素化，可以检验由此得到的扭转圈的非平凡性。利用这两种方法的组合，我们得到了生成某些数域的积分动上同调群的显式高周圈。
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英文标题：
《Functional equations of the dilogarithm in motivic cohomology》
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作者：
Oliver Petras
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最新提交年份：
2009
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分类信息：

一级分类：Mathematics        数学
二级分类：Number Theory        数论
分类描述：Prime numbers, diophantine equations, analytic number theory, algebraic number theory, arithmetic geometry, Galois theory
素数，丢番图方程，解析数论，代数数论，算术几何，伽罗瓦理论
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一级分类：Mathematics        数学
二级分类：Algebraic Geometry        代数几何
分类描述：Algebraic varieties, stacks, sheaves, schemes, moduli spaces, complex geometry, quantum cohomology
代数簇，叠，束，格式，模空间，复几何，量子上同调
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英文摘要：
  We prove relations between fractional linear cycles in Bloch's integral cubical higher Chow complex in codimension two of number fields, which correspond to functional equations of the dilogarithm.   These relations suffice, as we shall demonstrate with a few examples, to write down enough relations in Bloch's integral higher Chow group CH^2(F,3) for certain number fields F to detect torsion cycles.   Using the regulator map to Deligne cohomology, one can check the non-triviality of the torsion cycles thus obtained. Using this combination of methods, we obtain explicit higher Chow cycles generating the integral motivic cohomology groups of some number fields.
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PDF链接：
https://arxiv.org/pdf/0712.3987