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

@article{Lei2020OnTM,
title={On the Mordell-Weil ranks of supersingular abelian varieties in cyclotomic extensions},
author={Antonio Lei and Gautier Ponsinet},
journal={Proceedings of the American Mathematical Society, Series B},
year={2020}
}
• Published 19 July 2018
• Mathematics
• Proceedings of the American Mathematical Society, Series B
<p>Let <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper F"> <mml:semantics> <mml:mi>F</mml:mi> <mml:annotation encoding="application/x-tex">F</mml:annotation> </mml:semantics> </mml:math> </inline-formula> be a number field unramified at an odd prime <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="p"> <mml:semantics> <mml:mi>p</mml:mi> <mml…
7 Citations
Mordell–Weil ranks and Tate–Shafarevich groups of elliptic curves with mixed-reduction type over cyclotomic extensions
• Mathematics
International Journal of Number Theory
• 2021
Let [Formula: see text] be an elliptic curve defined over a number field [Formula: see text] where [Formula: see text] splits completely. Suppose that [Formula: see text] has good reduction at all
On the control theorem for fine Selmer groups and the growth of fine Tate-Shafarevich groups in $\mathbb{Z}_p$-extensions
Let $A$ be an abelian variety defined over a number field $F$. We prove a control theorem for the fine Selmer group of the abelian variety $A$ which essentially says that the kernel and cokernel of
On the Mordell-Weil Ranks of supersingular abelian varieties over $\mathbb{Z}_p^2$-extensions
• Mathematics
• 2021
Let p be a fixed odd prime and let K be an imaginary quadratic field in which p splits. Let A be an abelian variety defined over K with supersingular reduction at both primes above p in K. Under
Bounding the Iwasawa invariants of Selmer groups
Abstract We study the growth of p-primary Selmer groups of abelian varieties with good ordinary reduction at p in ${{Z}}_p$ -extensions of a fixed number field K. Proving that in many situations
Rational points on algebraic curves in infinite towers of number fields
. We study a natural question in the Iwasawa theory of algebraic curves of genus > 1 . Fix a prime number p . Let X be a smooth, projective, geometrically irreducible curve deﬁned over a number ﬁeld
Chromatic Selmer groups and arithmetic invariants of elliptic curves
Chromatic Selmer groups are modified Selmer groups with local information for supersingular primes p. We sketch their role in establishing the p-primary part of the Birch–Swinnerton-Dyer formula in