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2015 Transition formulae for ranks of abelian varieties
Daniel Delbourgo, Antonio Lei
Rocky Mountain J. Math. 45(6): 1807-1838 (2015). DOI: 10.1216/RMJ-2015-45-6-1807

Abstract

Let $A_{/k}$ denote an abelian variety defined over a number field $k$ with good ordinary reduction at all primes above $p$, and let $K_{\infty }=\bigcup _{n\geq 1} K_n$ be a $p$-adic Lie extension of $k$ containing the cyclotomic $\mathbb{Z}_p$-extension. We use $\mathrm {K}-theory to find recurrence relations for the $\lambda$-invariant at each $\sigma$-component of the Selmer group over $K_{\infty }$, where $\sigma :G_k\rightarrow \mathrm{GL}(V)$. This provides upper bounds on the Mordell-Weil rank for $A(K_n)$ as $n\rightarrow \infty$ whenever $G_{\infty }=\mathrm {Gal}(K_{\infty}/k)$ has dimension at most $3$.

Citation

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Daniel Delbourgo. Antonio Lei. "Transition formulae for ranks of abelian varieties." Rocky Mountain J. Math. 45 (6) 1807 - 1838, 2015. https://doi.org/10.1216/RMJ-2015-45-6-1807

Information

Published: 2015
First available in Project Euclid: 14 March 2016

zbMATH: 1355.11070
MathSciNet: MR3473156
Digital Object Identifier: 10.1216/RMJ-2015-45-6-1807

Subjects:
Primary: 11G10, 11R23, 20F05, 22E20

Rights: Copyright © 2015 Rocky Mountain Mathematics Consortium

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Vol.45 • No. 6 • 2015
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