# Davide Lombardo

1. On the $\ell$-adic Hodge group of nonsimple Abelian varieties

Annales de l'Institut Fourier, 66 no. 3 (2016), p. 1217–1245. Published version.

2. Bounds for Serre's open image theorem for elliptic curves over number fields

Algebra and Number Theory, 9–10 (2015), p. 2347–2395. Published version.

3. Explicit surjectivity for Galois representations attached to abelian surfaces

Journal of Algebra, volume 460, 15 August 2016, p. 26–59. Published version.

4. Roots of unity and torsion points of abelian varieties

Ramanujan Journal 2016. Published version.

5. An explicit open image theorem for products of elliptic curves

Journal of Number Theory, Volume 168, November 2016, p. 386–412. Published version.

6. Pink-type results for general subgroups of $\operatorname{SL}_2(\mathbb{Z}_\ell)^n$

Journal de Théorie des Nombres de Bordeaux, 29 no. 1 (2017), p. 85–127. Published version.

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

Rendiconti Lincei - Matematica e Applicazioni, Volume 28, Issue 1, 2017, p. 65–83. Published version.

8. The 1-eigenspace for matrices in $\operatorname{GL}_2(\mathbb{Z}_\ell)$ (joint with A. Perucca)

New York Journal of Mathematics, 23:897–925, 2017. Published version.

9. Galois representations attached to abelian varieties of CM type

Accepted for publication in the Bulletin de la Société Mathématique de France.
10. Accepted for publication in Mathematical Research Letters.

11. Accepted for publication in Mathematics of Computation.

Click here to download an implementation of the algorithms described in the paper and tables of results. Here is some more specific MAGMA code to compute elliptic subcovers of a given genus 2 curve.