l-TORSION BOUNDS FOR THE CLASS GROUP OF NUMBER FIELDS WITH AN l-GROUP AS GALOIS GROUP

被引：7

作者：

Klueners, Jurgen ^{[1
]}

Wang, Jiuya ^{[2
]}

机构：

[1] Univ Paderborn, Inst Math, Warburger Str 100, D-33098 Paderborn, Germany

[2] Univ Georgia, Boyd Grad Studies Res Ctr, Dept Math, Athens, GA 30601 USA

来源：

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY | 2022年 / 150卷 / 07期

关键词：

EXTENSIONS;

D O I：

10.1090/proc/15882

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We describe the relations among the l-torsion conjecture, a conjecture of Malle giving an upper bound for the number of extensions, and the discriminant multiplicity conjecture. We prove that the latter two conjectures are equivalent in some sense. Altogether, the three conjectures are equivalent for the class of solvable groups. We then prove the l-torsion conjecture for l-groups and the other two conjectures for nilpotent groups.

引用

页码：2793 / 2805

页数：13

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