Introduces a fiber-summation inductive method that proves new cases of Malle's conjecture and gives counterexamples to Malle's predicted exponents for wreath products.
Pointwise Bound for $\ell$-torsion in Class Groups II: Nilpotent Extensions
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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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2025 1verdicts
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Inductive methods for counting number fields
Introduces a fiber-summation inductive method that proves new cases of Malle's conjecture and gives counterexamples to Malle's predicted exponents for wreath products.