Davide Lombardo

Attività didattica

Incarichi di responsabilità didattica di moduli/insegnamenti

Registro lezioni

Orario lezioni

Interessi di ricerca

The main focus of my research is the arithmetic of abelian varieties and the study of their associated Galois representations (in the spirit of the Mumford-Tate and Sato-Tate conjectures). This comprises questions ranging from pure arithmetic geometry (can we find a good description of the effect of base change on the Néron model of a non-semistable abelian variety?) to computational problems (how does one determine the endomorphism ring of the Jacobian of a nice curve over the rationals?). I'm also interested in effective methods for the determination of integral or rational points on algebraic varieties (e.g., modular curves).

Pubblicazioni

• On the L-polynomials of curves over finite fields (Ballini, Francesco; Lombardo, Davide; Verzobio, Matteo - 2025 - 1.1 Articolo in rivista)
• Non-isogenous abelian varieties sharing the same division fields (Lombardo, D - 2023 - 1.1 Articolo in rivista)
• On the distribution of rational points on ramified covers of abelian varieties (Corvaja, P; Demeio, Jl; Javanpeykar, A; Lombardo, D; Zannier, U - 2022 - 1.1 Articolo in rivista)
• Effective Kummer Theory for Elliptic Curves (Lombardo, Davide; Tronto, Sebastiano - 2022 - 1.1 Articolo in rivista)
• Decomposing Jacobians Via Galois covers (Lombardo, D.; Garcia, E. L.; Ritzenthaler, C.; Sijsling, J. - 2021 - 1.1 Articolo in rivista)
• Reductions of points on algebraic groups (Lombardo, Davide; Perucca, Antonella - 2021 - 1.1 Articolo in rivista)
• Abelian Varieties as Automorphism Groups of Smooth Projective Varieties (Lombardo, Davide; Maffei, Andrea - 2020 - 1.1 Articolo in rivista)
• Computing the geometric endomorphism ring of a genus 2 Jacobian (Lombardo, Davide - 2019 - 1.1 Articolo in rivista)
• On the l-adic Galois representations attached to nonsimple abelian varieties (Lombardo, Davide - 2016 - 1.1 Articolo in rivista)
• Bounds for Serre's open image theorem for elliptic curves over number fields (Lombardo, Davide - 2015 - 1.1 Articolo in rivista)

Tutte le pubblicazioni di Davide Lombardo su ARPI, l'archivio della Ricerca dell'Università di Pisa