ℓ-torsion bounds for the class group of number fields with an ℓ-group as Galois group
J Klüners, J Wang - Proceedings of the American Mathematical Society, 2022 - ams.org
We describe the relations among the $\ell $-torsion conjecture, a conjecture of Malle giving
an upper bound for the number of extensions, and the discriminant multiplicity conjecture …
an upper bound for the number of extensions, and the discriminant multiplicity conjecture …
On Malle's conjecture for nilpotent groups
P Koymans, C Pagano - … of the American Mathematical Society, Series B, 2023 - ams.org
We develop an abstract framework for studying the strong form of Malle's conjecture [J.
Number Theory 92 (2002), pp. 315–329; Experiment. Math. 13 (2004), pp. 129–135] for …
Number Theory 92 (2002), pp. 315–329; Experiment. Math. 13 (2004), pp. 129–135] for …
On Stevenhagen's conjecture
P Koymans, C Pagano - arXiv preprint arXiv:2201.13424, 2022 - arxiv.org
We generalize a classical reciprocity law due to R\'edei using our recently developed
description of the $2 $-torsion of class groups of multiquadratic fields. This result is then …
description of the $2 $-torsion of class groups of multiquadratic fields. This result is then …
On the p-Rank of Class Groups of p-Extensions
Y Liu - International Mathematics Research Notices, 2024 - academic.oup.com
We prove a local–global principle for the embedding problems of global fields with restricted
ramification. By this local–global principle, for a global field, we use only the local …
ramification. By this local–global principle, for a global field, we use only the local …
On the Distribution of Class Groups of Abelian Extensions
Y Liu - arXiv preprint arXiv:2411.19318, 2024 - arxiv.org
Given a finite abelian group $\Gamma $, we study the distribution of the $ p $-part of the
class group $\operatorname {Cl}(K) $ as $ K $ varies over Galois extensions of $\mathbb {Q} …
class group $\operatorname {Cl}(K) $ as $ K $ varies over Galois extensions of $\mathbb {Q} …