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Explicit non-Gorenstein $$R={\mathbb {T}}$$ via rank bounds II: Computational aspects

https://doi.org/10.1007/s40993-022-00401-1

Hsu, Catherine; Wake, Preston; Wang-Erickson, Carl (March 2023, Research in Number Theory)

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A modular construction of unramified 𝑝-extensions of ℚ(ℕ^{1/𝕡})

https://doi.org/10.1090/bproc/141

Lang, Jaclyn; Wake, Preston (October 2022, Proceedings of the American Mathematical Society, Series B)

We show that for primes $N, p \geq<#comment/> 5$ with $N \equiv<#comment/> -<#comment/> 1 mod p$ , the class number of $Q (N^{1 / p})$ is divisible by $p$ . Our methods are via congruences between Eisenstein series and cusp forms. In particular, we show that when $N \equiv<#comment/> -<#comment/> 1 mod p$ , there is always a cusp form of weight $2$ and level ${Γ<#comment/>}_{0} (N^{2})$ whose $ℓ<#comment/>$ th Fourier coefficient is congruent to $ℓ<#comment/> + 1$ modulo a prime above $p$ , for all primes $ℓ<#comment/>$ . We use the Galois representation of such a cusp form to explicitly construct an unramified degree- $p$ extension of $Q (N^{1 / p})$ .
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Another look at rational torsion of modular Jacobians

https://doi.org/10.1073/pnas.2210032119

Ribet, Kenneth A.; Wake, Preston (October 2022, Proceedings of the National Academy of Sciences)

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The Eisenstein ideal for weight k and a Bloch–Kato conjecture for tame families

https://doi.org/10.4171/JEMS/1251

Wake, Preston (June 2022, Journal of the European Mathematical Society)

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The Eisenstein ideal with squarefree level

https://doi.org/10.1016/j.aim.2020.107543

Wake, Preston; Wang-Erickson, Carl (March 2021, Advances in Mathematics)

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The rank of Mazur’s Eisenstein ideal

https://doi.org/10.1215/00127094-2019-0039

Wake, Preston; Wang-Erickson, Carl (January 2020, Duke Mathematical Journal)

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