Number Theory Seminar
Schedule 2025/26
| Speaker | Title of the talk | Date | Time & place |
|---|---|---|---|
| Sara Checcoli | A little bit of little points generated by torsion | 22.09 | TBA |
Abstracts 2025/26
Sara Checcoli, A little bit of little points generated by torsion
The height is a non-negative real-valued function that measures the arithmetic complexity of an algebraic number. While numbers of minimal height are well understood, many questions remain about numbers of small but non-zero height. One such question is whether a given algebraic extension K of the rationals contains only finitely many elements of bounded height, in which case, following Bombieri and Zannier, K is said to have the Northcott property (N). While this holds for number fields, the situation is more subtle for infinite extensions of the rationals. For example, the maximal abelian extension of the rationals does not have (N), but it follows from a result of Bombieri and Zannier that its subextensions with Galois group of bounded exponent do. In this talk, after giving an overview on the subject, I will present joint work with Gabriel Dill establishing, in particular, a similar result for fields generated by torsion points of abelian varieties over number fields.