Unlikely intersections for curves in additive groups over positive characteristic

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. Recently the second author made a start on removing this restriction by studying multiplicative groups over positivecharacteristic, and here we go further for additive groups with extra Frobenius structure. We state a conjecture for curves in general dimension and we prove it in three dimensions. We also give an example where the finite set in question can be explicitly determined

Zero estimates with moving targets

Zero estimates have a classical history in diophantine approximation and transcendence, as well as more recent applications to counting rational points on analytic sets. We give some examples showing that the sharpest conceivable results can be false, and in some cases the natural guess has even to be doubled. A by-product is a "non-degenerate" case of the (unproved) "Zilber Nullstellensatz" in connexion with "Strong Exponential Closure"