# Item

ITEM ACTIONSEXPORT

Released

Journal Article

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

##### External Ressource

https://doi.org/10.1090/bproc/43

(Publisher version)

##### Fulltext (public)

Lei-Ponsinet_On the Mordell-Weil ranks of supersingular abelian varieties in cyclotomic extensions_2020.pdf

(Publisher version), 269KB

##### 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.