Unlikely intersections for curves in additive groups over positive characteristic

Brownawell, W.; Masser, D.

doi:10.1090/proc/13617

Unlikely intersections for curves in additive groups over positive characteristic
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by W. D. Brownawell and D. W. Masser

Proc. Amer. Math. Soc. 145 (2017), 4617-4627

DOI: https://doi.org/10.1090/proc/13617

Published electronically: May 26, 2017

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Abstract:

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 positive characteristic, 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.

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