D. Lombardo

activity

20162021

collaborators

7 papers

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.AG2020

Decomposing Jacobians via Galois covers

Davide Lombardo, Elisa Lorenzo García, Christophe Ritzenthaler +1

Let $ϕ : X \to Y$ be a (possibly ramified) cover between two algebraic curves of positive genus. We develop tools that may identify the Prym variety of $ϕ$ , up to isogeny, a…

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.AG2018

Abelian varieties as automorphism groups of smooth projective varieties

Davide Lombardo, Andrea Maffei

We determine which complex abelian varieties can be realized as the automorphism group of a smooth projective variety.