CORDIS Project
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This research project investigates the arithmetic properties of curves, focusing on rational points, their classification, and connections to conjectures in number theory. It employs advanced mathematical techniques to explore various families of curves and aims to provide insights into longstanding conjectures in the…
The study of the arithmetic of curves is as old as mathematics itself and takes on many forms.
In some cases, such as Fermat's Last Theorem or Mazur's torsion theorem, one tries to prove that a sequence of curves with growing genus has no interesting rational points.
In other cases, such as the study of rational points in families of elliptic curves, there is no way to classify all solutions, but one tries to understand what is happening on average. A third approach aims to link the existence…
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