An explicit family of cubic number fields with large $2$-rank of the class group

Avinash Kulkarni

An explicit family of cubic number fields with large $2$-rank of the class group

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arxiv 1610.07668 v2 pith:QJSVA7ZE submitted 2016-10-24 math.NT

Avinash Kulkarni This is my paper · ORCID

classification math.NT

keywords classcubicfamilyfieldsgroupnumberconstructdegree

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abstract

We show how to construct infinite families of explicitly determined cubic number fields whose class group has a subgroup isomorphic to $(\mathbb{Z}/2)^8$ using degree $1$ del Pezzo surfaces. We illustrate the method and provide an example of such a family.

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Lower bounds on the $\ell$-rank of ideal class groups
math.NT 2025-01 accept novelty 8.0 of 10

For ℓ-divisible extensions K/F, the ℓ-rank of the class group of K is at least the number of base primes with at least one ℓ-divisible ramification index, divided by a group invariant, corrected by unit ranks and the ...

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