On ℓ-torsion in class groups of number fields

  title={On ℓ-torsion in class groups of number fields},
  author={Jordan S. Ellenberg and L. B. Pierce and Melanie Matchett Wood},
  journal={Algebra \& Number Theory},
For each integer $\ell \geq 1$, we prove an unconditional upper bound on the size of the $\ell$-torsion subgroup of the class group, which holds for all but a zero-density set of field extensions of $\mathbb{Q}$ of degree $d$, for any fixed $d \in \{2,3,4,5\}$ (with the additional restriction in the case $d=4$ that the field be non-$D_4$). For sufficiently large $\ell$ (specified explicitly), these results are as strong as a previously known bound that is conditional on GRH. As part of our… 
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