Ranks of elliptic curves over Z_p^2-extensions

Abstract

Let $E$ be an elliptic curve with good reduction at a fixed odd prime $p$ and $K$ an imaginary quadratic field where $p$ splits. We give a growth estimate for the Mordell-Weil rank of $E$ over finite extensions inside the ${\mathbb{Z}}_p^2$-extension of $K$.

arXiv comment15 pages, plus references

References in corpus (4)

• On the asymptotic growth of Bloch-Kato-Shafarevich-Tate groups of modular forms over cyclotomic extensions
• The Iwasawa Main Conjecture for elliptic curves at odd supersingular primes
• Factorisation of two-variable p-adic L-functions
• On the Iwasawa main conjectures for modular forms at non-ordinary primes

Cited by in corpus (2)

• On the growth of Mordell-Weil ranks in $p$-adic Lie extensions
• Mordell-Weil ranks and Tate-Shafarevich groups of elliptic curves with mixed-reduction type over cyclotomic extensions