D. Lombardo

activity

20152026

most citedGalois representations attached to abelian varieties of CM type

3 citations · 3 across the 9 of their papers we have counts for

collaborators

9 papers

math.NT2026

Interpolation determinants and the Lebesgue--Nagell equation $a^{2} - D = b^{p}$

Davide Lombardo

We prove the long-standing conjecture that, for every odd prime $p$ , the only integral solutions of $a^{2} - 2 = b^{p}$ are $(a, b) = (\pm 1, - 1)$ . We also completely solve the analogous equa…

math.NT2026

Equationless quadratic Chabauty for non-split Cartan modular curves

Sachi Hashimoto, Guido Maria Lido, Davide Lombardo +2

The aim of this article is to describe an equationless method for determining the rational points on the non-split Cartan curve $X_{ns}^{+} (N)$ of prime level $N ⩾ 13$ .…

math.NT2026

Explicit p-adic Hodge theory for elliptic curves and non-split Cartan images

Matthew Bisatt, Lorenzo Furio, Davide Lombardo

Let $E / Q_{p}$ be an elliptic curve whose mod $p$ Galois image is contained in the normaliser of a non-split Cartan. We classify the possible $p$ -adic images of $E$ using too…

math.AG2025

Cohomology of varieties over the maximal Kummer extension of a number field

Davide Lombardo, Tamás Szamuely

Let $X$ be a smooth projective geometrically connected variety defined over a number field $K$ . We prove that the geometric étale cohomology of $X$ with $Q / Z$ -coe…

math.NT2025

Connected monodromy fields of Jacobians with complex multiplication

Andrea Gallese, Davide Lombardo

We describe an algorithm to compute the minimal field of definition of the Tate classes on powers of a Jacobian $J$ with potential complex multiplication. This field arises as a na…

math.NT2025

Monodromy groups and exceptional Hodge classes, II: Sato-Tate groups

Andrea Gallese, Heidi Goodson, Davide Lombardo

Denote by $J_{m}$ the Jacobian variety of the hyperelliptic curve defined by the affine equation $y^{2} = x^{m} + 1$ over $Q$ , where $m \geq 3$ is a fixed positive integer. In this…

math.NT2025

On 7-adic Galois representations for elliptic curves over $Q$

Lorenzo Furio, Davide Lombardo

In recent years, significant progress has been made on Mazur's Program B, with many authors beginning a systematic classification of all possible images of $p$ -adic Galois represen…

math.NT2024

Monodromy groups and exceptional Hodge classes, I: Fermat Jacobians

Andrea Gallese, Heidi Goodson, Davide Lombardo

Denote by $J_{m}$ the Jacobian variety of the hyperelliptic curve defined by the affine equation $y^{2} = x^{m} + 1$ over $Q$ , where $m \geq 3$ is a fixed positive integer. We compu…

math.NT2015★ 3 cited

Galois representations attached to abelian varieties of CM type

Davide Lombardo

Let $K$ be a number field, $A / K$ be an absolutely simple abelian variety of CM type, and $ℓ$ be a prime number. We give explicit bounds on the degree over $K$ of the division fi…

Interpolation determinants and the Lebesgue--Nagell equation a2−D=bp

Equationless quadratic Chabauty for non-split Cartan modular curves

Explicit p-adic Hodge theory for elliptic curves and non-split Cartan images

Cohomology of varieties over the maximal Kummer extension of a number field

Connected monodromy fields of Jacobians with complex multiplication

Monodromy groups and exceptional Hodge classes, II: Sato-Tate groups

On 7-adic Galois representations for elliptic curves over Q

Monodromy groups and exceptional Hodge classes, I: Fermat Jacobians

Galois representations attached to abelian varieties of CM type

Interpolation determinants and the Lebesgue--Nagell equation $a^{2} - D = b^{p}$

On 7-adic Galois representations for elliptic curves over $Q$