整等价数域的对应 Abel 扩张
Corresponding Abelian Extensions of Integrally Equivalent Number Fields
AI总结：
本文研究整等价数域的 Abel 扩张诱导对应，利用 idelic 类域论和线性代数证明其扩张特征类似算术等价域但通常非弱 Kronecker 等价，并扩展群上同调结果给出几何与算术应用。
摘要：
为了确定数域的 Abel 扩张双射对应迫使基域同构的充要条件，已有大量研究。然而，非同构域上对应的显式例子十分罕见。整等价数域允许 Abel 扩张的诱导对应。利用 idelic 类域论和线性代数研究这一对应，我们表明相应的扩张具有与算术等价域相似的特征，但通常并非弱 Kronecker 等价。我们还扩展了 Arapura 等人的群上同调结果，并给出了几何与算术应用。
英文摘要：
Extensive work has been done to determine necessary and sufficient conditions for a bijective correspondence of abelian extensions of number fields to force an isomorphism of the base fields. However, explicit examples of correspondences over non-isomorphic fields are rare. Integrally equivalent number fields admit an induced correspondence of abelian extensions. Studying this correspondence using idelic class field theory and linear algebra, we show that the corresponding extensions share features similar to those of arithmetically equivalent fields, and yet they are not generally weakly Kronecker equivalent. We also extend a group cohomological result of Arapura et. al. and present geometric and arithmetic applications.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
