Remote Access Proceedings of the American Mathematical Society Series B
Gold Open Access

Proceedings of the American Mathematical Society Series B

ISSN 2330-1511

   
 
 

 

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


Authors: Antonio Lei and Gautier Ponsinet
Journal: Proc. Amer. Math. Soc. Ser. B 7 (2020), 1-16
MSC (2010): Primary 11R23; Secondary 11G10, 11R18
DOI: https://doi.org/10.1090/bproc/43
Published electronically: February 11, 2020
MathSciNet review: 4062429
Full-text PDF Open Access
View in AMS MathViewer New

Abstract | References | Similar Articles | Additional Information

Abstract: Let $F$ be a number field unramified at an odd prime $p$ and let $F_\infty$ 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 $p$. Büyükboduk 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 is a torsion $\mathbf {Z}_p[[\textrm {Gal}(F_\infty /F)]]$-module, we give an explicit sufficient condition for the rank of the Mordell-Weil group $A(F_n)$ to be bounded as $n$ varies.


References [Enhancements On Off] (What's this?)

References

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society, Series B with MSC (2010): 11R23, 11G10, 11R18

Retrieve articles in all journals with MSC (2010): 11R23, 11G10, 11R18


Additional Information

Antonio Lei
Affiliation: Département de Mathématiques et de Statistiques, Université Laval, Pavillon Alexandre-Vachon, 1045 Avenue de la Médecine, Québec, Quebec, Canada G1V 0A6
MR Author ID: 902727
ORCID: 0000-0001-9453-3112
Email: antonio.lei@mat.ulaval.ca

Gautier Ponsinet
Affiliation: Max Planck Institut for Mathematics, Vivatsgasse 7, 53111 Bonn, Germany
MR Author ID: 1210959
Email: gautier.ponsinet@mpim-bonn.mpg.de

Keywords: Iwasawa theory, supersingular primes, abelian varieties, Mordell-Weil ranks
Received by editor(s): July 19, 2018
Received by editor(s) in revised form: August 20, 2018, March 27, 2019, and May 21, 2019
Published electronically: February 11, 2020
Additional Notes: The authors’ research was supported by the NSERC Discovery Grants Program 05710.
Communicated by: Romyar T. Sharifi
Article copyright: © Copyright 2020 by the authors under Creative Commons Attribution 3.0 License (CC BY 3.0)