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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Unlikely intersections for curves in additive groups over positive characteristic
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by W. D. Brownawell and D. W. Masser PDF
Proc. Amer. Math. Soc. 145 (2017), 4617-4627 Request permission

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.
References
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Additional Information
  • W. D. Brownawell
  • Affiliation: Department of Mathematics, The Pennsylvania State University, University Park, Pennsylvania 16802
  • MR Author ID: 42245
  • Email: wdb@math.psu.edu
  • D. W. Masser
  • Affiliation: Departement Mathematik und Informatik, Universität Basel, Spiegelgasse 1, 4051 Basel, Switzerland
  • MR Author ID: 121080
  • Email: David.Masser@unibas.ch
  • 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
  • © Copyright 2017 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 145 (2017), 4617-4627
  • MSC (2010): Primary 11G20, 14G17, 14H99
  • DOI: https://doi.org/10.1090/proc/13617
  • MathSciNet review: 3691981