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Research group in Diophantine Geometry

Gruppo di ricerca di Geometria Diofantea

Research areas of the group

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.