TY - JOUR
AB - 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.
AU - Klüners, Jürgen
AU - Wang, Jiuya
ID - 34839
IS - 7
JF - Proceedings of the American Mathematical Society
KW - Applied Mathematics
KW - General Mathematics
SN - 0002-9939
TI - ℓ-torsion bounds for the class group of number fields with an ℓ-group as Galois group
VL - 150
ER -