For every number field K and every integer ℓ≥2, the ℓ-torsion of the class group is o_{[K:Q],ℓ}(|Disc K|^{1/2}), with an explicit log-power saving.
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Improving the trivial bound for $\ell$-torsion in class groups
For every number field K and every integer ℓ≥2, the ℓ-torsion of the class group is o_{[K:Q],ℓ}(|Disc K|^{1/2}), with an explicit log-power saving.