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

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.

13 pages; small changes and corrections made in v2; comments and corrections welcome