论文标题
Arakelov的随机数字段组
Arakelov class groups of random number fields
论文作者
论文摘要
本文的主要目的是为Arakelov阶级组制定概率模型，以对理想班级组的Cohen-Lenstra--Martinet启发式进行纠正。为此，我们表明Chinburg的Omega（3）猜想意味着对定向Arakelov阶级组的Galois模块结构的严格限制。结果，我们为Cohen-Lenstra-Martinet启发式构建了一系列新的无限反例，该样本具有新颖的特征，即他们的Galois群体是非亚伯利亚人。
The main purpose of the paper is to formulate a probabilistic model for Arakelov class groups in families of number fields, offering a correction to the Cohen--Lenstra--Martinet heuristic on ideal class groups. To that end, we show that Chinburg's Omega(3) conjecture implies tight restrictions on the Galois module structure of oriented Arakelov class groups. As a consequence, we construct a new infinite series of counterexamples to the Cohen--Lenstra--Martinet heuristic, which have the novel feature that their Galois groups are non-abelian.
