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), pp. 469-501. Published version.

  10. On the uniform Rasmussen-Tamagawa conjecture in the CM case. Mathematical Research Letters Volume 25, No. 6 (2018), pp. 1893-1910. Online version

  11. Computing the geometric endomorphism ring of a genus-2 Jacobian. Mathematics of Computation, 88 (2019), pp. 889-929. Published version.

    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), pp. 991-1022. Published version.

  13. Abelian varieties as automorphism groups of smooth projective varieties (joint with Andrea Maffei). International Mathematics Research Notices (IMRN), Volume 2020, Issue 7, April 2020, Pages 1942–1956. Published version.

  14. Computing twists of hyperelliptic curves (joint with Elisa Lorenzo García). Here is some MAGMA code to compute the twist of a particular genus-5 curve. Journal of Algebra, Volume 519, 1 February 2019, pp. 474-490. Published version.

  15. Appendix to Surjectivity of Galois representations in rational families of abelian varieties (by A. Landesman, A. Swaminathan, J. Tao, Y. Xu). Algebra and Number Theory 13(5): 995-1038 (2019).

  16. Reductions of points on commutative algebraic groups (joint with A. Perucca). Journal of the Institute of Mathematics of Jussieu 2021;20(5):1637-1669. Published version

  17. Identifying central endomorphisms of an abelian variety via Frobenius endomorphisms (joint with E. Costa and J. Voight). Research in Number Theory, 2021, 7:46. Published version.

  18. Decomposing Jacobians via Galois covers (joint with Elisa Lorenzo García, Christophe Ritzenthaler, and Jeroen Sijsling). Experimental Mathematics 32:1 (2023), 218-240. Published version.

  19. Explicit Kummer theory for elliptic curves (joint with Sebastiano Tronto). International Mathematics Research Notes, Volume 2022, Issue 22, November 2022, Pages 17662–17712. Published version

  20. How far is an extension of p-adic fields from having a normal integral basis? (joint with Ilaria del Corso and Fabio Ferri). Journal of Number Theory, Volume 233, April 2022, Pages 158-197. Published version

  21. Local opers with two singularities: the case of $\mathfrak{sl}(2)$ (joint with Giorgia Fortuna, Andrea Maffei and Valerio Melani). Communications in Mathematical Physics 394, 1303–1360 (2022). Published version

  22. Non-isogenous abelian varieties sharing the same division fields. Transactions of the AMS 376 (2023), 2615-2640. Published version

  23. On the distribution of rational points on ramified covers of abelian varieties (joint with Pietro Corvaja, Julian L. Demeio, Ariyan Javanpeykar and Umberto Zannier). Compositio Mathematica 2022;158(11):2109-2155. Published version

  24. Some uniform bounds for elliptic curves over $\mathbb{Q}$ (joint with Sebastiano Tronto). Pacific Journal of Mathematics, Vol. 320 (2022), No. 1, 133–175. Published version

  25. A family of quintic Thue equations via Skolem's $p$-adic method. Rivistica di Matematica della Università di Parma 13 (2022), no. 1, 161-173.

  26. The semi-infinite cohomology of Weyl modules with two singular points (joint with Giorgia Fortuna, Andrea Maffei and Valerio Melani). Pure and Applied Mathematics Quarterly. Published version

  27. On the local-global principle for isogenies of abelian surfaces (joint with Matteo Verzobio). Here is some computer code accompanying the paper. Selecta Mathematica, published online.

Proceedings

  1. Galois representations in arithmetic geometry (Atti del XXII Congresso Nazionale UMI, September 2023)

Preprints

  1. Explicit open image theorems for abelian varieties with trivial endomorphism ring

  2. On the $L$-polynomials of curves over finite fields

  3. Torsion bounds for a fixed abelian variety and varying number field (joint with Samuel Le Fourn and David Zywina)
    The paper references a letter by David Masser that is not easily available online. Professor Masser has been kind enough to let me take pictures of his copy of the letter and make them available here.

  4. Monodromy groups of Jacobians with definite quaternionic multiplication (joint with Victoria Cantoral Farfán and John Voight)

  5. Cohomology of groups acting on vector spaces over finite fields (joint with Laura Paladino)

  6. Serre's uniformity question and proper subgroups of $C^+_{ns}(p)$ (joint with Lorenzo Furio)

  7. Classification of rational angles in plane lattices II (joint with Roberto Dvornicich, Francesco Veneziano and Umberto Zannier)

  8. Monodromy groups and exceptional Hodge classes (joint with Andrea Gallese and Heidi Goodson)

  9. Examples of effectivity for integral points on certain curves of genus 2 (joint with Pietro Corvaja and Umberto Zannier)