Davide Lombardo

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Research interests

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).

Publications

• 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)

All publications by Davide Lombardo on ARPI, the Research Archive of the University of Pisa