Mordell-Weil growth for GL2-type abelian varieties over Hilbert class fields of CM fields

TL;DR

This paper investigates the growth of the Mordell-Weil rank of GL2-type modular abelian varieties over Hilbert class fields of CM extensions, demonstrating polynomial growth under certain conditions.

Contribution

It establishes the polynomial growth of Mordell-Weil ranks for a class of abelian varieties over specific number field extensions, under mild assumptions.

Findings

Mordell-Weil rank grows polynomially over Hilbert class fields

Results apply to GL2-type modular abelian varieties

Growth behavior depends on mild assumptions

Abstract

Let A be a modular abelian variety of GL2-type over a totally real field F of class number one. Under some mild assumptions, we show that the Mordell-Weil rank of A grows polynomially over Hilbert class fields of CM extensions of F.