Ahmed Matar

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20172026

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math.NT2026

Vanishing of $Sha (A / K) [P^{\infty}]$ and its consequences for the anticyclotomic Iwasawa theory of $GL_{2}$ -abelian varieties

Luca Mastella, Ahmed Matar, Francesco Zerman

In this article we generalise a classical Kolyvagin's result on the vanishing of the $p$ -part of the Shafarevich--Tate group of an elliptic curve (defined over $Q$ ) over a…

math.NT2026

On the $M_{H} (G)$ -property for Selmer groups at supersingular reduction

Sören Kleine, Ahmed Matar, Sujatha Ramdorai

Let $E$ be an elliptic curve defined over $Q$ which has good supersingular reduction at the odd prime $p$ . We study the variation of Iwasawa invariants and the $\mathfrak{…

math.NT2018

On the Lambda-cotorsion subgroup of the Selmer group

Ahmed Matar

Let $E$ be an elliptic curve defined over a number field $K$ with supersingular reduction at all primes of $K$ above $p$ . If $K_{\infty} / K$ is a $Z_{p}$ -extension such that…

math.NT2018

Kolyvagin's result on the vanishing of $\sha(E/K)[p^\infty]$ and its consequences for anticyclotomic Iwasawa theory

Ahmed Matar, Jan Nekovar

Let $E$ be an elliptic curve defined over $Q$ and $K$ an imaginary quadratic field satisfying the Heegner hypothesis. A classical result of Kolyvagin states that, under suita…

math.NT2017

On the Fine Selmer Group

Ahmed Matar

Let $E / Q$ be an elliptic curve, $p$ an odd prime and $K_{\infty} / K$ the anticyclotomic $Z_{p}$ -extension of a quadratic imaginary field $K$ . In a previous article t…

Vanishing of Sha(A/K)[P∞] and its consequences for the anticyclotomic Iwasawa theory of GL2​-abelian varieties

On the MH​(G)-property for Selmer groups at supersingular reduction

On the Lambda-cotorsion subgroup of the Selmer group

Kolyvagin's result on the vanishing of $\sha(E/K)[p^\infty]$ and its consequences for anticyclotomic Iwasawa theory

On the Fine Selmer Group

Vanishing of $Sha (A / K) [P^{\infty}]$ and its consequences for the anticyclotomic Iwasawa theory of $GL_{2}$ -abelian varieties

On the $M_{H} (G)$ -property for Selmer groups at supersingular reduction