Math @ Duke

Publications [#320660] of Lillian B. Pierce
Papers Published
 Ellenberg, J; Pierce, L; Wood, M, On ℓtorsion in class groups of number
fields,
Algebra & Number Theory, vol. 11 no. 8
(2017),
pp. 17391778, Mathematical Sciences Publishers [doi]
(last updated on 2019/01/23)
Abstract: © 2017 Mathematical Sciences Publishers. For each integer ℓ ≥ 1, we prove an unconditional upper bound on the size of the ℓtorsion subgroup of the class group, which holds for all but a zerodensity set of field extensions of Q of degree d, for any fixed d ε {2; 3; 4; 5} (with the additional restriction in the case d D 4 that the field be nonD 4 ). For sufficiently large ℓ (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, powersaving error terms for the asymptotics of quartic (nonD 4 ) and quintic fields with chosen splitting types at a finite set of primes.


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