S. Vigni

works on

euler systems 1 hida families 1 iwasawa theory 1 p-adic l-functions 1 selmer groups 1 symmetric square 1

From the 1 of 7 linked papers with an AI index.

activity

20242026

collaborators

7 papers

math.NT2026

Analytic rank one propagation in Hida families

Stefano Vigni

Let $f$ be a non-CM newform of weight $k \geq 4$ , level $N$ and trivial Nebentypus. Let $p ∤ N$ be an odd prime number that is ordinary for $f$ and denote by $f^{(p)}$ …

math.NT2026

Euler systems and the symmetric square of a Hida family

Debanjana Kundu, Jishnu Ray, Stefano Vigni

The paper constructs a non‑trivial Euler system for the symmetric square of a p‑adic Hida family of modular forms, proves an algebraic functional equation for the associated dual S…

math.NT2026

Anticyclotomic Iwasawa main conjectures for modular forms

Matteo Longo, Maria Rosaria Pati, Stefano Vigni

Let $f$ be a newform of even weight at least $4$ , level $N$ and trivial character. Let $p ∤ N$ be an odd prime number that is ordinary for $f$ and let $K$ be an imaginary quadra…

math.NT2026

Higher Fitting ideals and the structure of anticyclotomic Shafarevich-Tate groups

Enrico Da Ronche, Matteo Longo, Stefano Vigni

Let $p$ be a prime number. We investigate a refined version of the Iwasawa main conjectures for rational elliptic curves (and more general Galois representations) over anticyclotom…

math.NT2025

On anticyclotomic Selmer groups of elliptic curves

Matteo Longo, Jishnu Ray, Stefano Vigni

Let $p \geq 5$ be a prime number and let $K$ be an imaginary quadratic field where $p$ is unramified. Under mild technical assumptions, in this paper we prove the non-existence of no…

math.NT2025

A generalized Rubin formula for Hecke characters

Matteo Longo, Stefano Vigni, Shilun Wang

The goal of this paper is to generalize Rubin's theorem on values of Katz's $p$ -adic $L$ -function outside the range of interpolation from the case of Hecke characters of CM ellipti…