l-Torsion Bounds for the Class Group of Number Fields with an l -Group as Galois Group
MFO Scientific ProgramResearch in Pairs 2019
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We describe the relations among the $\ell$-torsion conjecture for $\ell$-extensions, the discriminant multiplicity conjecture for nilpotent extensions and a conjecture of Malle giving an upper bound for the number of nilpotent extensions. We then prove all of these conjectures in these cases.