Francesco Zerman

collaborators

4 papers

math.NT2026

Variation of Shafarevich-Tate groups in Hida families

Enrico Da Ronche, Matteo Longo, Stefano Vigni +1

Let $f$ be a Hida family of cusp forms over a standard (power series) Iwasawa algebra. We determine the pseudo-isomorphism class of the big Shafarevich-Tate group attached…

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.NT2025

Quaternionic Kolyvagin systems and Iwasawa theory for Hida families

Francesco Zerman

We build a modified universal Kolyvagin system for the Galois representation attached to a Hida family of modular forms, starting from the big Heegner point Euler system of Longo--…

math.NT2025

On anticyclotomic Euler and Kolyvagin systems

Luca Mastella, Francesco Zerman

We introduce an axiomatization of the notion of ( $p$ -complete) anticyclotomic Euler system for a wide class of Galois representations, including those attached to a cuspidal eigen…

Variation of Shafarevich-Tate groups in Hida families

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

Quaternionic Kolyvagin systems and Iwasawa theory for Hida families

On anticyclotomic Euler and Kolyvagin systems

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