Maria Rosaria Pati

activity

20152026

most citedExtensions of degree p^l of a p-adic field

2 citations · 2 across the 7 of their papers we have counts for

collaborators

8 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

On Shafarevich-Tate groups and analytic ranks in families of modular forms, II. Coleman families

Maria Rosaria Pati, Gautier Ponsinet, Stefano Vigni

This is the second article in a two-part project whose aim is to study algebraic and analytic ranks in $p$ -adic families of modular forms. Let $f$ be a newform of weight $2$ , squar…

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…

math.NT2015★ 2 cited

Extensions of degree p^l of a p-adic field

Maria Rosaria Pati

Given a $p$ -adic field $K$ and a prime number $ℓ$ , we count the total number of the isomorphism classes of $p^{ℓ}$ -extensions of $K$ having no intermediate fields. Moreover for…