most citedRank stability in quadratic extensions and Hilbert's tenth problem for the ring of integers of a number field

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math.NT2025★ 1 cited

Rank stability in quadratic extensions and Hilbert's tenth problem for the ring of integers of a number field

Levent Alpöge, Manjul Bhargava, Wei Ho +1

We show that for any quadratic extension of number fields , there exists an abelian variety of positive rank whose rank does not grow upon base change to . This resul…

math.NT2020

A positive proportion of cubic fields are not monogenic yet have no local obstruction to being so

Levent Alpöge, Manjul Bhargava, Ari Shnidman

We show that a positive proportion of cubic fields are not monogenic, despite having no local obstruction to being monogenic. Our proof involves the comparison of -descent and $…