Delbourgo, D., & Lei, A. (2015). Transition formulae for ranks of abelian varieties. Rocky Mountain Journal of Mathematics, 45(6), 1807–1838. http://doi.org/10.1216/RMJ-2015-45-6-1807
Permanent Research Commons link: http://hdl.handle.net/10289/10021
Let A/k denote an abelian variety defined over a number field k with good ordinary reduction at all primes above p, and let K∞ =∪n≥1 Kn be a p-adic Lie extension of k containing the cyclotomic Zp-extension. We use K-theory to find recurrence relations for the λ-invariant at each σ-component of the Selmer group over K∞, where σ : Gk → GL(V ). This provides upper bounds on the Mordell-Weil rank for A(Kn) as n → ∞ whenever G∞ = Gal(K∞/k) has dimension at most 3.
Rocky Mountain Mathematics Consortium
This article is published in the Rocky Mountain Journal of Mathematics. Used with permission.