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On the Mordell-Weil ranks of supersingular abelian varieties in cyclotomic extensions

MPS-Authors
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Ponsinet,  Gautier
Max Planck Institute for Mathematics, Max Planck Society;

External Ressource

https://doi.org/10.1090/bproc/43
(Publisher version)

Supplementary Material (public)
There is no public supplementary material available
Citation

Lei, A., & Ponsinet, G. (2020). On the Mordell-Weil ranks of supersingular abelian varieties in cyclotomic extensions. Proceedings of the American Mathematical Society. Series B, 2020(7), 1-16. doi:10.1090/bproc/43.


Cite as: http://hdl.handle.net/21.11116/0000-0007-EE6B-6
Abstract
Let $F$ be a number field unramified at an odd prime $p$ and $F_\infty$ be the $\mathbf{Z}_p$-cyclotomic extension of $F$. Let $A$ be an abelian variety defined over $F$ with good supersingular reduction at all primes of $F$ above $p$. B\"uy\"ukboduk and the first named author have defined modified Selmer groups associated to $A$ over $F_\infty$. Assuming that the Pontryagin dual of these Selmer groups are torsion $\mathbf{Z}_p[[\mathrm{Gal}(F_\infty/F)]]$-modules, we give an explicit sufficient condition for the rank of the Mordell-Weil group $A(F_n)$ to be bounded as $n$ varies.