Research group in Diophantine Geometry
Research areas of the group are:
- Full points on curves and other algebraic varieties: problems of finiteness and of parameterization of the points under study. Application of techniques of Diophantine Approximation, in particular of Schmidt's Subspace Theorem.
- Diophantine Equations on number fields and function fields. Issues of effective determination of the solutions.
- Height of algebraic points on subvarieties of varieties of group.
- Linear dependence of points on subvarieties of varieties of group; problems connected to intersections of subvarieties fixed with algebraic subgroups in opportune families (e.g., data dimension).
- Irreducibility of polynoms on number fields and function fields; analogues of the Bertini Theorem for algebraic groups. Issues about Hilbert's Irreducibility Theorem.