GENERALISED MAZUR’S GROWTH NUMBER CONJECTURE

Abstract Let F be a totally real field. Let $\mathsf {A}$ be a simple modular self-dual abelian variety defined over F . We study the growth of the corank of Selmer groups of $\mathsf {A}$ over $\mathbb {Z}_p$ -extensions of a complex multiplication (CM) extension of F . We propose an extension of Mazur’s growth number conjecture for elliptic curves to this new setting. We provide evidence supporting an affirmative answer by studying special cases of this problem, generalising previous results on elliptic curves and imaginary quadratic fields.