# 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).HÃ¶rmann, 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).