论文标题
一些对称的金字塔，琐碎的dehn不变
Some Symmetric Pyramids with trivial Dehn invariant
论文作者
论文摘要
对于某些$ r^3 $的对称金字塔，我们发现galois的dehn不变性为零，即金字塔等于剪刀等同于立方体。这些条件是，数字字段的一些相关的Kummer扩展必须是Abelian。这项工作可以看作是[5]的补充。实际上，在[5]中，给出了所有理性四面体的分类，而我们将注意力集中在更对称的金字塔上，并证明唯一与立方体相等的剪刀是理性的。
For some symmetric pyramids of $R^3$ , we find Galois obstruction for their Dehn invariant to be zero, i.e. for the pyramids to be scissor equivalent to a cube. These conditions are that some associated Kummer extensions of number fields must be abelian. This work can be viewed as a complement to [5]. Indeed, in [5], a classification of all rational tetrahedra is given, while we concentrate our attention on much more symmetric pyramids and prove that the only ones which are scissor equivalent to a cube are the rational ones.
