On -unramified extensions over imaginary quadratic fields

Pub Date : 2023-11-29 DOI:10.1017/s001708952300037x

Kwang-Seob Kim, Joachim König

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引用次数: 0

Abstract

Let

$n$

be an integer congruent to

$0$

$3$

modulo

$4$

. Under the assumption of the ABC conjecture, we prove that, given any integer

$m$

fulfilling only a certain coprimeness condition, there exist infinitely many imaginary quadratic fields having an everywhere unramified Galois extension of group

$A_n \times C_m$

. The same result is obtained unconditionally in special cases.

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虚二次域上的非分枝扩展

设$n$是一个整数，等于$0$或$3$取$4$的模。在ABC猜想的假设下，证明了给定任意整数$m$满足一定的协素性条件，则存在无穷多个虚二次域，它们具有群$A_n \乘以C_m$的处处无分枝伽罗瓦扩展。在特殊情况下也可以无条件地得到同样的结果。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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