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Unlikely intersections for curves in additive groups over positive characteristic


Authors: W. D. Brownawell and D. W. Masser
Journal: Proc. Amer. Math. Soc. 145 (2017), 4617-4627
MSC (2010): Primary 11G20, 14G17, 14H99
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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Additional Information

W. D. Brownawell
Affiliation: Department of Mathematics, The Pennsylvania State University, University Park, Pennsylvania 16802
Email: wdb@math.psu.edu

D. W. Masser
Affiliation: Departement Mathematik und Informatik, Universität Basel, Spiegelgasse 1, 4051 Basel, Switzerland
Email: David.Masser@unibas.ch

DOI: https://doi.org/10.1090/proc/13617
Received by editor(s): October 9, 2016
Received by editor(s) in revised form: November 30, 2016
Published electronically: May 26, 2017
Communicated by: Matthew A. Papanikolas
Article copyright: © Copyright 2017 American Mathematical Society