Laura Paladino

activity

20112025

most citedPreperiodic points for rational functions defined over a global field in terms of good reductions

3 citations · 4 across the 14 of their papers we have counts for

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16 papers · 1 filter

math.NT2025

On the Hasse principle for divisibility in elliptic curves

Jessica Alessandrì, Laura Paladino

Let $p$ be a prime number and $n$ a positive integer. Let $E$ be an elliptic curve defined over a number field $k$ . It is known that the local-global divisibility by $p$ holds in $…

math.NT2023

A survey of local-global methods for Hilbert's Tenth Problem

Sylvy Anscombe, Valentijn Karemaker, Zeynep Kisakürek +3

Hilbert's Tenth Problem (H10) for a ring R asks for an algorithm to decide correctly, for each $f \in Z [X_{1}, \dots, X_{n}]$ , whether the diophantine equation $f(X_{1},...,X_…

math.NT2023

Testing local-global divisibility at a stable set

Alexander B. Ivanov, Laura Paladino

We show that the local-global divisibility in commutative algebraic groups defined over number fields can be tested on sets of primes of arbitrary small density, i.e. stable and pe…

math.NT2023

Local-global divisibility on algebraic tori

Jessica Alessandrì, Rocco Chirivì, Laura Paladino

We give a complete answer to the local-global divisibility problem for algebraic tori. In particular, we prove that given an odd prime $p$ , if $T$ is an algebraic torus of dimensio…

math.NT2021

On 7-division fields of CM elliptic curves

Jessica Alessandrì, Laura Paladino

Let $E$ be a CM elliptic curve defined over a number field $K$ , with Weiestrass form $y^{3} = x^{3} + b x$ or $y^{2} = x^{3} + c$ . For every positive integer $m$ , we denote by ${\mathcal{…

math.NT2020

Cohomology of groups acting on vector spaces over finite fields

Davide Lombardo, Laura Paladino

Let $F_{q}$ be the finite field with $q = p^{m}$ elements and $G$ be a subgroup of $GL_{n} (F_{q})$ . A famous theorem of Nori published in 1987 states that there…

math.NT2020

On the division fields of an elliptic curve and an effective bound to the hypotheses of the local-global divisibility

Roberto Dvornicich, Laura Paladino

We investigate some aspects of the $m$ -division field $K (E [m])$ , where $E$ is an elliptic curve defined over a field $K$ with $char (K) \neq = 2, 3$ and…

math.NT2018

On 5-torsion of CM elliptic curves

Laura Paladino

Let $E$ be an elliptic curve defined over a number field $K$ . Let $m$ be a positive integer. We denote by $E [m]$ the $m$ -torsion subgroup of $E$ and…

math.NT2017

Local-global questions for divisibility in commutative algebraic groups

Roberto Dvornicich, Laura Paladino

This is a survey focusing on the Hasse principle for divisibility of points in commutative algebraic groups and its relation with the Hasse principle for divisibility of elements o…

math.NT2016

Divisibility questions in commutative algebraic groups

Laura Paladino

Let $k$ be a number field, let $A$ be a commutative algebraic group defined over $k$ and let $p$ be a prime number. Let $A [p]$ denote the $p$ -torsion subgro…

math.NT2016

On preperiodic points of rational functions defined over $F_{p} (t)$

Jung Kyu Canci, Laura Paladino

Let $P \in P_{1} (Q)$ be a periodic point for a monic polynomial with coefficients in $Z$ . With elementary techniques one sees that the minimal periodicity of…

math.NT2014

Fields generated by torsion points of elliptic curves

Andrea Bandini, Laura Paladino

Let K be a number field and let $E$ be an elliptic curve defined over $K$ . Let $m$ be a positive integer. We denote by $K (E [m])$ the number fields obtained by a…

math.NT2014★ 3 cited

Preperiodic points for rational functions defined over a global field in terms of good reductions

Jung-Kyu Canci, Laura Paladino

Let $ϕ$ be an endomorphism of the projective line defined over a global field $K$ . We prove a bound for the cardinality of the set of $K$ -rational preperiodic points for $ϕ$ in ter…

math.NT2011

On the minimal set for counterexamples to the local-global principle

Laura Paladino, Gabriele Ranieri, Evelina Viada

We prove that only for powers of 2 and 3 could occur counterexamples to the local-global divisibility principle for elliptic curves defined over the rationals. For we refine our pr…

math.NT2011★ 1 cited

On local-global divisibility by $p^{n}$ in elliptic curves

Laura Paladino, Gabriele Ranieri, Evelina Viada

Let $p$ be a prime number and let $k$ be a number field, which does not contain the field $Q (ζ_{p} + ζ_{p} ˉ)$ . Let $E$ be an elliptic curve defined over $k$ .…

math.NT2011

On local-global divisibility by $p^{2}$ in elliptic curves

Laura Paladino, Gabriele Ranieri, Evelina Viada

Let $p$ be a prime lager than 3. Let $k$ be a number field, which does not contain the subfield of $Q (ζ_{p^{2}})$ of degree $p$ over $Q$ . Suppose that $\mathcal{…

On the Hasse principle for divisibility in elliptic curves

A survey of local-global methods for Hilbert's Tenth Problem

Testing local-global divisibility at a stable set

Local-global divisibility on algebraic tori

On 7-division fields of CM elliptic curves

Cohomology of groups acting on vector spaces over finite fields

On the division fields of an elliptic curve and an effective bound to the hypotheses of the local-global divisibility

On 5-torsion of CM elliptic curves

Local-global questions for divisibility in commutative algebraic groups

Divisibility questions in commutative algebraic groups

On preperiodic points of rational functions defined over Fp​(t)

Fields generated by torsion points of elliptic curves

Preperiodic points for rational functions defined over a global field in terms of good reductions

On the minimal set for counterexamples to the local-global principle

On local-global divisibility by pn in elliptic curves

On local-global divisibility by p2 in elliptic curves

On preperiodic points of rational functions defined over $F_{p} (t)$

On local-global divisibility by $p^{n}$ in elliptic curves

On local-global divisibility by $p^{2}$ in elliptic curves