On the growth of Mordell–Weil ranks in $p$-adic Lie extensions
On the growth of Mordell–Weil ranks in $p$-adic Lie extensions
Let $p$ be an odd prime and $F_{\infty}$ a $p$-adic Lie extension of a number field $F$. Let $A$ be an abelian variety over $F$ which has ordinary reduction at every primes above $p$. Under various assumptions, we establish asymptotic upper bounds for the growth of Mordell-Weil rank of the …