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arXiv · 2006.10295

Pointwise Bound for $\ell$-torsion in Class Groups II: Nilpotent Extensions

Jiuya Wang
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Abstract

For every finite $p$-group $G_p$ that is non-cyclic and non-quaternion and every positive integer $\ell\neq p$ that is greater than $2$, we prove the first non-trivial bound on $\ell$-torsion in class group of every $G_p$-extension. More generally, for every nilpotent group $G$ where every Sylow-$p$ subgroup $G_p\subset G$ is non-cyclic and non-quaternion, we prove a non-trivial bound on $\ell$-torsion in class group of every $G$-extension for every integer $\ell>1$.

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Jiuya Wang. 2020-06-18. Pointwise Bound for $\ell$-torsion in Class Groups II: Nilpotent Extensions. https://arxiv.org/abs/2006.10295

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