Maria Rosaria Pati

activity

20172026

collaborators

6 papers

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.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.NT2023

On the Iwasawa Main Conjecture for generalized Heegner classes in a quaternionic setting

Maria Rosaria Pati

We prove one divisibility relation of the anticyclotomic Iwasawa Main Conjecture for a higher weight ordinary modular form $f$ and an imaginary quadratic field satisfying a "relaxe…

math.NT2021

L-invariants for cohomological representations of PGL(2) over arbitrary number fields

Lennart Gehrmann, Maria Rosaria Pati

Let $π$ be a cuspidal, cohomological automorphic representation of an inner form $G$ of $PGL_{2}$ over a number field $F$ of arbitrary signature. Further, let $p$ …

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.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…