On the Mordell-Weil ranks of supersingular abelian varieties in cyclotomic extensions
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- by Antonio Lei and Gautier Ponsinet HTML | PDF
- Proc. Amer. Math. Soc. Ser. B 7 (2020), 1-16
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
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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
- 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
- © Copyright 2020 by the authors under Creative Commons Attribution 3.0 License (CC BY 3.0)
- 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
- MathSciNet review: 4062429