Number Theory
Cluster
- Algebra and Geometry
Description
The research is mainly carried out within the Diophantine Geometry, that is within the theory of Diophantine equations, dealt with from a geometric point of view. In particular, Vojta's conjectures are studied, linking the distribution of rational and integer points on algebraic varieties with geometric invariants of the varieties themselves, such as the canonical bundle.
Other themes dealt with are the so-called property of Hilbert, linked with Hilbert's irreducibility theorem, which was studied outside the classical scope of the unirational varieties, too.
There are links with the algebraic geometry and the complex analytical geometry, concerning issues such as the algebraic and analytical hyperbolicity: the study of rational points on higher dimensional varieties naturally brings to the study of rational algebraic curves or of holomorphic curves in those varieties.
Another theme that is dealt with is that of the torsion by sections of abelian schemes and the consequent study of the relevant Betti Map.
ERC panels
- PE1_3 Number theory
- PE1_4 Algebraic and complex geometry
Tags
- Diophantine equations, Diophantine approximation, arithmetic geometry
- Algebraic groups, Nevanlinna theory