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math.NT2021
Betti maps, Pell equation in polynomials and almost Belyi maps
Fabrizio Barroero, Laura Capuano, Umberto Zannier
We study the Betti map of a particular (but relevant) section of the family of Jacobians of hyperelliptic curves using the polynomial Pell equation , with $A,B,D\in \ma…
math.NT2021
Unlikely Intersections of Curves with Algebraic Subgroups in Semiabelian Varieties
Fabrizio Barroero, Lars Kühne, Harry Schmidt
Let be a semiabelian variety and a curve in that is not contained in a proper algebraic subgroup of . In this situation, conjectures of Pink and Zilber imply that th…
math.NT2021★ 2 cited
Distinguished categories and the Zilber-Pink conjecture
Fabrizio Barroero, Gabriel Andreas Dill
We propose an axiomatic approach towards studying unlikely intersections by introducing the framework of distinguished categories. This includes commutative algebraic groups and mi…