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The distribution of $\ell^{\infty}$-Selmer groups in degree $\ell$ twist families II

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arxiv 2207.05143 v2 pith:F77NTORG submitted 2022-07-11 math.NT

Alexander Smith This is my paper · ORCID
classification math.NT
keywords groupsselmertwistdegreedistributioninftyfamiliesfamily
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abstract

We continue the investigation of the distribution of $\ell^{\infty}$-Selmer groups in degree $\ell$ twist families of Galois modules over number fields begun in the previous paper. Building off the work on higher Selmer groups in that part, we find conditions under which we can compute the distribution of the $\ell^{\infty}$-Selmer groups for a given degree $\ell$ twist family. Along the way, we show that the average rank in the quadratic twist family of any given abelian variety over a number field is bounded.

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Cited by 4 Pith papers

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