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The conjectures associated with the names of Zilber–Pink greatly generalize results associated with the names of Manin–Mumford and Mordell–Lang, but unlike the latter they are at present restricted to zero characteristic. We make a start on removing this restriction by stating a conjecture for curves in multiplicative groups over positive characteristic, and we verify the conjecture in three dimensions as well as for some special lines in general dimension. We also give an example where the finite set in question can be explicitly determined.

UNLIKELY INTERSECTIONS FOR CURVES IN MULTIPLICATIVE GROUPS OVER POSITIVE CHARACTERISTIC