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Publications (34)

math.NT2016

Kolyvagin systems and Iwasawa theory of generalized Heegner cycles

Matteo Longo, Stefano Vigni

Iwasawa theory of Heegner points on abelian varieties of GL_2 type has been studied by, among others, Mazur, Perrin-Riou, Bertolini and Howard. The purpose of this paper is to desc…

math.NT2019

Generalized Heegner cycles on Mumford curves

Matteo Longo, Maria Rosaria Pati

We study generalised Heegner cycles, originally introduced by Bertolini-Darmon-Prasanna for modular curves, in the context of Mumford curves. The main result of this paper relates…

math.NT2024

A $p$ -adic adjoint $L$ -function and the ramification locus of the Hilbert modular eigenvariety

Baskar Balasubramanyam, John Bergdall, Matteo Longo

Let $F$ be a totally real field and $E$ the middle-degree eigenvariety for Hilbert modular forms over $F$ , constructed by Bergdall--Hansen. We study the ramification locu…

math.NT2019

The $p$ -adic variation of the Gross-Kohnen-Zagier theorem

Matteo Longo, Marc-Hubert Nicole

We relate $p$ -adic families of Jacobi forms to Big Heegner points constructed by B. Howard, in the spirit of the Gross-Kohnen-Zagier theorem. We view this as a GL(2) instance of a…

math.NT2026

The anticyclotomic main conjectures for elliptic curves

Massimo Bertolini, Matteo Longo, Rodolfo Venerucci

The goal of this article is to obtain a proof of the Main conjectures of Iwasawa theory for rational elliptic curves over anticyclotomic extensions of imaginary quadratic fields, u…

math.NT2023

The Tamagawa number conjecture and Kolyvagin's conjecture for motives of modular forms

Matteo Longo, Stefano Vigni

Assuming specific instances of two general conjectures in arithmetic algebraic geometry (bijectivity of $p$ -adic regulator maps, injectivity of $p$ -adic Abel-Jacobi maps), we prove…

math.NT2026

On the local-global principle for twists of abelian varieties and Galois representations

Nirvana Coppola, Lorenzo La Porta, Matteo Longo

This paper investigates the validity of a local-global principle for finite twists of a large class of objects endowed with a continuous action of the absolute Galois group of a gi…

math.NT2013

A refined Beilinson-Bloch conjecture for motives of modular forms

Matteo Longo, Stefano Vigni

We propose a refined version of the Beilinson-Bloch conjecture for the motive associated with a modular form of even weight. This conjecture relates the dimension of the image of t…

math.NT2011

A note on control theorems for quaternionic Hida families of modular forms

Matteo Longo, Stefano Vigni

We extend a result of Greenberg and Stevens on the interpolation of modular symbols in Hida families to the context of non-split rational quaternion algebras. Both the definite cas…

math.NT2026

On quaternionic ordinary families of modular forms and $p$ -adic $L$ -functions

Matteo Longo, Paola Magrone, Eris Rocha Walchek

We use Serre--Tate expansions of modular forms to construct power series attached to quaternionic ordinary families of modular forms. We associate to these power series a big $p$ -a…

math.NT2026

Quaternionic families of Heegner points and $p$ -adic $L$ -functions

Matteo Longo, Paola Magrone, Eris Rocha Walchek

Following up a previous article of the authors which studies the interpolation of certain anticyclotomic $p$ -adic $L$ -functions associated to quaternionic modular forms in a Hida f…

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…

math.NT2020

Rationality of Darmon points over genus fields of non-maximal orders

Matteo Longo, Kimball Martin, Yan Hu

Stark-Heegner points, also known as Darmon points, were introduced by H. Darmon as certain local points on rational elliptic curves, conjecturally defined over abelian extensions o…

math.NT2024

Kolyvagin's conjecture for modular forms

Matteo Longo, Maria Rosaria Pati, Stefano Vigni

Our main result in this article is a proof (under mild technical assumptions) of an analogue for $p$ -adic Galois representations attached to a newform $f$ of even weight $k \geq 4$ o…

math.NT2018

Variation of anticyclotomic Iwasawa invariants in Hida families

Francesc Castella, Chan-Ho Kim, Matteo Longo

Building on the construction of big Heegner points in the quaternionic setting, and their relation to special values of Rankin-Selberg $L$ -functions, we obtain anticyclotomic analo…

math.NT2025

Big Heegner points, generalized Heegner classes and $p$ -adic $L$ -functions in the quaternionic setting

Matteo Longo, Paola Magrone, Eduardo Rocha Walchek

The goal of this paper is to study the $p$ -adic variation of Heegner points and generalized Heegner classes for ordinary families of quaternionic modular forms. We compare classica…

math.NT2023

An explicit comparison of anticyclotomic $p$ -adic $L$ -functions for Hida families

Chan-Ho Kim, Matteo Longo

The aim of this note is to compare several anticyclotomic $p$ -adic $L$ -functions for modular forms and $p$ -adic families of ordinary modular forms, which have been defined and stud…

math.NT2020

On Bloch-Kato Selmer groups and Iwasawa theory of $p$ -adic Galois representations

Matteo Longo, Stefano Vigni

A result due to R. Greenberg gives a relation between the cardinality of Selmer groups of elliptic curves over number fields and the characteristic power series of Pontryagin duals…

math.NT2016

Galois structure on integral valued polynomials

Bahar Heidaryan, Matteo Longo, Giulio Peruginelli

We characterize finite Galois extensions $K$ of the field of rational numbers in terms of the rings $Int_{Q} (O_{K})$ , recently introduced by Loper and Werner,…

math.NT2020

A p-adic Shimura-Maass operator on Mumford curves

Matteo Longo

We study a p-adic Shimura-Maass operator in the context of Mumford curves defined by C. Franc is his Ph.D. Thesis. We prove that this operator arises from a splitting of the Hodge…

math.NT2013

The Lambda-adic Shimura-Shintani-Waldspurger Correspondence

Matteo Longo, Marc-Hubert Nicole

We generalize the $I^$ -adic Shintani lifting for $G L_{2} (Q)$ to indefinite quaternion algebras over $Q$ .

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.NT2014

Big Heegner points and special values of $L$ -series

Francesc Castella, Matteo Longo

In \cite{LV}, Howard's construction of big Heegner points on modular curves was extended to general Shimura curves over the rationals. In this paper, we relate the higher weight sp…

math.NT2023

Anticyclotomic main conjecture and the non-triviality of Rankin-Selberg $L$ -values in Hida families

Chan-Ho Kim, Matteo Longo

The aim of this paper is to prove the two-variable anticyclotomic Iwasawa main conjecture for Hida families and a definite version of the horizontal non-vanishing conjecture, which…

math.NT2012

The Saito-Kurokawa lifting and Darmon points

Matteo Longo, Marc-Hubert Nicole

Let $E_{/_\Q}$ be an elliptic curve of conductor $N p$ with $p ∤ N$ and let $f$ be its associated newform of weight 2. Denote by $f_{\infty}$ the $p$ -adic Hida family passing thoug…

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.NT2016

Heegner points on Hijikata-Pizer-Shemanske curves

Matteo Longo, Victor Rotger, Carlos de Vera-Piquero

We study Heegner points on elliptic curves, or more generally modular abelian varieties, coming from uniformization by Shimura curves attached to a rather general type of quaternio…

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.NT2020

$I^$ -adic Families of Jacobi Forms

Matteo Longo, Marc-Hubert Nicole

We show that Hida's families of $p$ -adic elliptic modular forms generalize to $p$ -adic families of Jacobi forms. We also construct $p$ -adic versions of theta lifts from elliptic mo…

math.NT2015

Plus/minus Heegner points and Iwasawa theory of elliptic curves at supersingular primes

Matteo Longo, Stefano Vigni

Let $E$ be an elliptic curve over $Q$ and let $p \geq 5$ be a prime of good supersingular reduction for $E$ . Let $K$ be an imaginary quadratic field satisfying a modified "He…

math.NT2011

Special values of L-functions and the arithmetic of Darmon points

Matteo Longo, Victor Rotger, Stefano Vigni

Building on our previous work on rigid analytic uniformizations, we introduce Darmon points on Jacobians of Shimura curves attached to quaternion algebras over Q and formulate conj…

math.NT2014

Iwasawa theory of Heegner cycles, I. Rank over the Iwasawa algebra

Matteo Longo, Stefano Vigni

Iwasawa theory of Heegner points on abelian varieties of GL_2 type has been studied by, among others, Mazur, Perrin-Riou, Bertolini and Howard. The purpose of this paper, the first…

math.NT2012

Vanishing of special values and central derivatives in Hida families

Matteo Longo, Stefano Vigni

The theme of this work is the study of the NekovÃ¡Å-Selmer group H^1_f(K,T) attached to a twisted Hida family T of Galois representations and a quadratic number field K. The resul…

math.NT2017

Exceptional zero formulae for anticyclotomic p-adic L-functions of elliptic curves in the ramified case

Matteo Longo, Maria Rosaria Pati

Iwasawa theory of modular forms over anticyclotomic $Z_{p}$ -extensions of imaginary quadratic fields has been studied by several authors, starting from the works of Bertolin…

Publications (34)

Kolyvagin systems and Iwasawa theory of generalized Heegner cycles

Generalized Heegner cycles on Mumford curves

A p-adic adjoint L-function and the ramification locus of the Hilbert modular eigenvariety

The p-adic variation of the Gross-Kohnen-Zagier theorem

The anticyclotomic main conjectures for elliptic curves

The Tamagawa number conjecture and Kolyvagin's conjecture for motives of modular forms

On the local-global principle for twists of abelian varieties and Galois representations

A refined Beilinson-Bloch conjecture for motives of modular forms

A note on control theorems for quaternionic Hida families of modular forms

On quaternionic ordinary families of modular forms and p-adic L-functions

Quaternionic families of Heegner points and p-adic L-functions

A generalized Rubin formula for Hecke characters

Rationality of Darmon points over genus fields of non-maximal orders

Kolyvagin's conjecture for modular forms

Variation of anticyclotomic Iwasawa invariants in Hida families

Big Heegner points, generalized Heegner classes and p-adic L-functions in the quaternionic setting

An explicit comparison of anticyclotomic p-adic L-functions for Hida families

On Bloch-Kato Selmer groups and Iwasawa theory of p-adic Galois representations

Galois structure on integral valued polynomials

A p-adic Shimura-Maass operator on Mumford curves

The Lambda-adic Shimura-Shintani-Waldspurger Correspondence

Anticyclotomic Iwasawa main conjectures for modular forms

Big Heegner points and special values of L-series

Anticyclotomic main conjecture and the non-triviality of Rankin-Selberg L-values in Hida families

The Saito-Kurokawa lifting and Darmon points

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

Heegner points on Hijikata-Pizer-Shemanske curves

On anticyclotomic Selmer groups of elliptic curves

I^-adic Families of Jacobi Forms

Plus/minus Heegner points and Iwasawa theory of elliptic curves at supersingular primes

Special values of L-functions and the arithmetic of Darmon points

Iwasawa theory of Heegner cycles, I. Rank over the Iwasawa algebra

Vanishing of special values and central derivatives in Hida families

Exceptional zero formulae for anticyclotomic p-adic L-functions of elliptic curves in the ramified case

A $p$ -adic adjoint $L$ -function and the ramification locus of the Hilbert modular eigenvariety

The $p$ -adic variation of the Gross-Kohnen-Zagier theorem

On quaternionic ordinary families of modular forms and $p$ -adic $L$ -functions

Quaternionic families of Heegner points and $p$ -adic $L$ -functions

Big Heegner points, generalized Heegner classes and $p$ -adic $L$ -functions in the quaternionic setting

An explicit comparison of anticyclotomic $p$ -adic $L$ -functions for Hida families

On Bloch-Kato Selmer groups and Iwasawa theory of $p$ -adic Galois representations

Big Heegner points and special values of $L$ -series

Anticyclotomic main conjecture and the non-triviality of Rankin-Selberg $L$ -values in Hida families

$I^$ -adic Families of Jacobi Forms