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Creators/Authors contains: "Wake, Preston"

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  1. ; ; (, Selecta Mathematica)
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  2. ; ; (, Research in Number Theory)
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  3. ; ; (, Research in Number Theory)
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  4. ; (, 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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  5. ; (, Proceedings of the National Academy of Sciences)
    We study the rational torsion subgroup of the modular Jacobian J 0 ( N ) for N a square-free integer. We give a proof of a result of Ohta on a generalization of Ogg’s conjecture: For a prime number p ∤ 6 N , the p -primary part of the rational torsion subgroup equals that of the cuspidal subgroup. Whereas previous proofs of this result used explicit computations of the cardinalities of these groups, we instead use their structure as modules for the Hecke algebra. 
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  6. ; (, Proceedings of the National Academy of Sciences)
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  7. (, Journal of the European Mathematical Society)
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  8. ; ; ; ; (, 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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  9. ; ; ; ; (, Forum of Mathematics, Sigma)
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  10. ; (, Advances in Mathematics)
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