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Creators/Authors contains: "Wake, Preston"

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  1. ; ; (, Selecta Mathematica)
    Free, publicly-accessible full text available February 1, 2026
  2. ; ; (, Research in Number Theory)
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  3. ; (, Proceedings of the American Mathematical Society, Series B)
    We show that for primes N , p ≥<#comment/> 5 N, p \geq 5 with N ≡<#comment/> −<#comment/> 1 mod p N \equiv -1 \bmod p , the class number of Q ( N 1 / p ) \mathbb {Q}(N^{1/p}) is divisible by p p . Our methods are via congruences between Eisenstein series and cusp forms. In particular, we show that when N ≡<#comment/> −<#comment/> 1 mod p N \equiv -1 \bmod p , there is always a cusp form of weight 2 2 and level Γ<#comment/> 0 ( N 2 ) \Gamma _0(N^2) whose ℓ<#comment/> \ell th Fourier coefficient is congruent to ℓ<#comment/> + 1 \ell + 1 modulo a prime above p p , for all primes ℓ<#comment/> \ell . We use the Galois representation of such a cusp form to explicitly construct an unramified degree- p p extension of Q ( N 1 / p ) \mathbb {Q}(N^{1/p}) . 
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  4. ; (, Proceedings of the National Academy of Sciences)
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  5. ; ; ; ; (, Forum of Mathematics, Sigma)
    Abstract Given a profinite group G of finite p -cohomological dimension and a pro- p quotient H of G by a closed normal subgroup N , we study the filtration on the Iwasawa cohomology of N by powers of the augmentation ideal in the group algebra of H . We show that the graded pieces are related to the cohomology of G via analogues of Bockstein maps for the powers of the augmentation ideal. For certain groups H , we relate the values of these generalized Bockstein maps to Massey products relative to a restricted class of defining systems depending on H . We apply our study to prove lower bounds on the p -ranks of class groups of certain nonabelian extensions of $$\mathbb {Q}$$ and to give a new proof of the vanishing of Massey triple products in Galois cohomology. 
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  6. (, Journal of the European Mathematical Society)
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  7. ; (, Advances in Mathematics)
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  8. ; (, Duke Mathematical Journal)
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