ERC Starting Grant · 2022
Arithmetic of Curves and Jacobians
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 of rational points on a given curve to the preponderance of points on the curve modulo larger and larger prime numbers. This is the idea behind the Birch and Swinnerton-Dyer conjecture, and its…
From the public funding record at EU CORDIS. Describes the funded project, not the reviews below.