Abstract
For each integer , we prove an unconditional upper bound on the size of the -torsion subgroup of the class group, which holds for all but a zero-density set of field extensions of of degree , for any fixed (with the additional restriction in the case that the field be non-). For sufficiently large (specified explicitly), these results are as strong as a previously known bound that is conditional on GRH. As part of our argument, we develop a probabilistic “Chebyshev sieve,” and give uniform, power-saving error terms for the asymptotics of quartic (non-) and quintic fields with chosen splitting types at a finite set of primes.
Citation
Jordan Ellenberg. Lillian Pierce. Melanie Wood. "On $\ell$-torsion in class groups of number fields." Algebra Number Theory 11 (8) 1739 - 1778, 2017. https://doi.org/10.2140/ant.2017.11.1739
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