Research

After obtaining a bachelor degree in Trento in 2016 I have completed the ALGANT Master Program (Milano and Leiden), with special focus on number theory and algebraic geometry. I then moved on to obtain a joint PhD at the universities of Luxembourg and Leiden, under the supervision of Antonella Perucca and Peter Bruin.

I have collected in this page the list of papers I puplished during my PhD, as well as theses (Bachelor, Master, PhD). See my talks page for a list of slides and notes of my talks.

Theses

• Phd thesis: Kummer theory for commutative algebraic groups. University of Luxembourg and University of Leiden, 2022. Supervisors: Antonella Perucca, Peter J. Bruin. [Thesis: pdf, 1.2Mb; Stellingen: pdf, 123Kb]

• Master thesis: The Brauer-Manin obstruction to strong approximation. University of Milan and University of Leiden, 2018. Supervisor: Martin J. Bright. [pdf, 800Kb]

• Bachelor thesis: Gruppi di Galois e gruppi fondamentali. University of Trento, 2016. Supervisor: Edoardo Ballico. [pdf, 444Kb]

Publications and preprints

• Tronto, Sebastiano. Division in modules and Kummer theory. arXiv preprint.

• Lombardo, Davide; Tronto, Sebastiano. Some uniform bounds for elliptic curves over Q. Pacific Journal of Mathematics, (2022).

• Lombardo, Davide; Tronto, Sebastiano. Effective Kummer theory for elliptic curves. International Mathematics Research Notices (2021).

• Hörmann, Fritz; Perucca, Antonella; Sgobba, Pietro; Tronto, Sebastiano. Explicit Kummer theory for quadratic fields. JP Journal of Algebra, Number Theory and Applications (2021).

• Perucca, Antonella; Sgobba, Pietro; Tronto, Sebastiano. The degree of Kummer extensions of number fields. International Journal of Number Theory (2021).

• Perucca, Antonella; Sgobba, Pietro; Tronto, Sebastiano. Kummer Theory for number fields via entanglement groups. Manuscripta Mathematica (2021).

• Tronto, Sebastiano. Radical entanglement for elliptic curves. arXiv preprint.

• Perucca, Antonella; Sgobba, Pietro; Tronto, Sebastiano. Kummer theory for number fields. Proceedings of the Roman Number Theory Association (2020).

• Perucca, Antonella; Sgobba, Pietro; Tronto, Sebastiano. Addendum to: Reductions of Algebraic integers. Journal of Number Theory (2020).

• Perucca, Antonella; Sgobba, Pietro; Tronto, Sebastiano. Explicit Kummer theory for the rational numbers. International Journal of Number Theory (2020).