通过在高斯有理数上定义的二次映射迭代数域塔

Pub Date : 2020-10-01 DOI:10.3792/PJAA.96.012

Yasushi Mizusawa, Kota Yamamoto

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引用次数: 2

摘要

:一个迭代的数域塔是通过一个有理图的迭代来添加一个基点的预像来构造的。定义在高斯数域上的某基本二次有理映射产生了这样一个塔，其中任意两个步都是相对双环双二次扩展。把这类塔作为z2扩展的类似物，我们用一些例子检验了沿塔的2-理想类数的宇称性。

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Iterated towers of number fields by a quadratic map defined over the Gaussian rationals

: An iterated tower of number ﬁelds is constructed by adding preimages of a base point by iterations of a rational map. A certain basic quadratic rational map deﬁned over the Gaussian number ﬁeld yields such a tower of which any two steps are relative bicyclic biquadratic extensions. Regarding such towers as analogues of Z 2 -extensions, we examine the parity of 2-ideal class numbers along the towers with some examples.

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