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 | References | Similar Articles | Additional Information

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