Assuming the weak Bombieri-Lang conjecture, we prove that a generalization of Hilbert’s irreducibility theorem holds for families of geometrically mordellic varieties (for instance, families of hyperbolic curves). As an application we prove that, assuming Bombieri-Lang, there are no polynomial bijections Q × Q → Q, completing a strategy originally suggested by T. Tao.
A HIGHER DIMENSIONAL HILBERT IRREDUCIBILITY THEOREM
Bresciani G.
2025-01-01
Abstract
Assuming the weak Bombieri-Lang conjecture, we prove that a generalization of Hilbert’s irreducibility theorem holds for families of geometrically mordellic varieties (for instance, families of hyperbolic curves). As an application we prove that, assuming Bombieri-Lang, there are no polynomial bijections Q × Q → Q, completing a strategy originally suggested by T. Tao.File in questo prodotto:
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