D. Lombardo

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20162021

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5 papers · 1 filter

math.NT2021

Non-isogenous abelian varieties sharing the same division fields

Davide Lombardo

Two abelian varieties $A_{1}, A_{2}$ over a number field $K$ are called strongly iso-Kummerian if the torsion fields $K (A_{1} [d])$ and $K (A_{2} [d])$ coincide for all $d \geq 1$ . For all $g…

math.NT2020

How far is an extension of $p$ -adic fields from having a normal integral basis?

Ilaria Del Corso, Fabio Ferri, Davide Lombardo

Let $L / K$ be a finite Galois extension of $p$ -adic fields with group $G$ . It is well-known that $O_{L}$ contains a free $O_{K} [G]$ -submodule of finite index. We stu…

math.NT2019

Explicit Kummer Theory for Elliptic Curves

Davide Lombardo, Sebastiano Tronto

Let $E$ be an elliptic curve defined over a number field $K$ , let $α \in E (K)$ be a point of infinite order, and let $N^{- 1} α$ be the set of $N$ -division points of $α$ in $E(\bar{K}…

math.NT2019

Identifying central endomorphisms of an abelian variety via Frobenius endomorphisms

Edgar Costa, Davide Lombardo, John Voight

Assuming the Mumford-Tate conjecture, we show that the center of the endomorphism ring of an abelian variety defined over a number field can be recovered from an appropriate inters…

math.NT2016

On the analytic bijections of the rationals in $[0, 1]$

Davide Lombardo

We carry out an arithmetical study of analytic functions $f : [0, 1] \to [0, 1]$ that by restriction induce a bijection $Q \cap [0, 1] \to Q \cap [0, 1]$ . The existenc…

Non-isogenous abelian varieties sharing the same division fields

How far is an extension of p-adic fields from having a normal integral basis?

Explicit Kummer Theory for Elliptic Curves

Identifying central endomorphisms of an abelian variety via Frobenius endomorphisms

On the analytic bijections of the rationals in [0,1]

How far is an extension of $p$ -adic fields from having a normal integral basis?

On the analytic bijections of the rationals in $[0, 1]$