We formulate function field analogues for the Zilber-Pink Conjecture and for the Bounded Height Conjecture. The ‘‘special’’ varieties in our formulation are varieties defined over the constant field. We prove our function field Zilber-Pink Conjecture for all subvarieties, and we prove our function field Bounded Height Conjecture for a certain class of curves. We explain that for our problems the algebraic groups are no longer ‘‘special’’; instead the relevant notion is the transcendence degree over the constant field of the field of definition for our varieties.
Cite this article
Zoé Chatzidakis, Dragos Ghioca, David Masser, Guillaume Maurin, Unlikely, likely and impossible intersections without algebraic groups. Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. 24 (2013), no. 4, pp. 485–501