sebastiano.tronto.net

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research.md (2811B)

      1 # Research
      2 
      3 After obtaining a bachelor degree in Trento in 2016 I have completed the
      4 [ALGANT](https://algant.eu) Master Program (Milano and Leiden), with
      5 special focus on number theory and algebraic geometry. I then moved on to
      6 obtain a joint PhD at the universities of Luxembourg and Leiden, under
      7 the supervision of [Antonella Perucca](http://antonellaperucca.net) and
      8 [Peter Bruin](https://www.math.leidenuniv.nl/~pbruin).
      9 
     10 I have collected in this page the list of papers I puplished during my PhD,
     11 as well as theses (Bachelor, Master, PhD). See [my talks page](../talks)
     12 for a list of slides and notes of my talks.
     13 
     14 ## Theses
     15 
     16 * Phd thesis: *Kummer theory for commutative algebraic groups*.
     17   University of Luxembourg and University of Leiden, 2022.
     18   Supervisors: Antonella Perucca, Peter J. Bruin.
     19   [Thesis: [pdf, 1.2Mb](phd-thesis.pdf);
     20   Stellingen: [pdf, 123Kb](stellingen.pdf)]
     21 
     22 * Master thesis: *The Brauer-Manin obstruction to strong approximation*.
     23   University of Milan and University of Leiden, 2018.
     24   Supervisor: Martin J. Bright.
     25   [[pdf, 800Kb](master-thesis.pdf)]
     26 
     27 * Bachelor thesis: *Gruppi di Galois e gruppi fondamentali*.
     28   University of Trento, 2016.
     29   Supervisor: Edoardo Ballico.
     30   [[pdf, 444Kb](bachelor-thesis.pdf)]
     31 
     32 ## Publications and preprints
     33 
     34 * Tronto, Sebastiano.
     35   *Division in modules and Kummer theory.*
     36   [arXiv preprint](https://arxiv.org/abs/2111.14363).
     37 
     38 * Lombardo, Davide; Tronto, Sebastiano.
     39   *Some uniform bounds for elliptic curves over Q.*
     40   [Pacific Journal of Mathematics, (2022)](https://msp.org/pjm/2022/320-1/p06.xhtml).
     41 
     42 * Lombardo, Davide; Tronto, Sebastiano.
     43   *Effective Kummer theory for elliptic curves.*
     44   International Mathematics Research Notices (2021).
     45 
     46 * Hörmann, Fritz; Perucca, Antonella; Sgobba, Pietro; Tronto, Sebastiano.
     47   *Explicit Kummer theory for quadratic fields.*
     48   JP Journal of Algebra, Number Theory and Applications (2021).
     49 
     50 * Perucca, Antonella; Sgobba, Pietro; Tronto, Sebastiano.
     51   *The degree of Kummer extensions of number fields.*
     52   International Journal of Number Theory (2021).
     53 
     54 * Perucca, Antonella; Sgobba, Pietro; Tronto, Sebastiano.
     55   *Kummer Theory for number fields via entanglement groups.*
     56   Manuscripta Mathematica (2021).
     57 
     58 * Tronto, Sebastiano.
     59   *Radical entanglement for elliptic curves.*
     60   [arXiv preprint](https://arxiv.org/abs/2009.08298).
     61 
     62 * Perucca, Antonella; Sgobba, Pietro; Tronto, Sebastiano.
     63   *Kummer theory for number fields.*
     64   Proceedings of the Roman Number Theory Association (2020).
     65 
     66 * Perucca, Antonella; Sgobba, Pietro; Tronto, Sebastiano.
     67   *Addendum to: Reductions of Algebraic integers.*
     68   Journal of Number Theory (2020).
     69 
     70 * Perucca, Antonella; Sgobba, Pietro; Tronto, Sebastiano.
     71   *Explicit Kummer theory for the rational numbers.*
     72   International Journal of Number Theory (2020).