# Davide Lombardo

## Publications

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, volume 43, Issue 2 (June 2017), p. 383–403. 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. Bulletin de la Société Mathématique de France, 145, fascicule 3 (2017), 469-501. Published version.

10. On the uniform Rasmussen-Tamagawa conjecture in the CM case. Accepted for publication in Mathematical Research Letters.

11. Computing the geometric endomorphism ring of a genus-2 Jacobian. 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.

12. The twisting Sato-Tate group of the curve $y^2=x^8-14x^4+1$ (joint with S. Arora, V. Cantoral-Farfán, A. Landesman, J. S. Morrow). Mathematische Zeitschrift, Volume 290, Issue 3-4 (2018), 991-1022. Published version.

13. Abelian varieties as automorphism groups of smooth projective varieties (joint with Andrea Maffei). To appear in International Mathematics Research Notices (IMRN). Online version.

14. Computing twists of hyperelliptic curves (joint with E. Lorenzo-Garcia). Here is some MAGMA code to compute the twist of a particular genus-5 curve. Journal of Algebra, in press. Online first.