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A dynamical version of the Mordell–Lang conjecture for the additive group

Part of: Arithmetic algebraic geometry Abelian varieties and schemes Complex dynamical systems

Published online by Cambridge University Press:  01 March 2008

D. Ghioca  and
T. J. Tucker
D. Ghioca
Affiliation:
Department of Mathematics and Computer Science, University of Lethbridge, 4401 University Drive, Lethbridge, AB, Canada T1K 3M4 (email: dragos.ghioca@uleth.ca)
T. J. Tucker
Affiliation:
Department of Mathematics, Hylan Building, University of Rochester, Rochester, NY 14627, USA (email: ttucker@math.rochester.edu)
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Abstract

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We prove a dynamical version of the Mordell–Lang conjecture in the context of Drinfeld modules. We use analytic methods similar to those employed by Skolem, Chabauty, and Coleman for studying diophantine equations.

Keywords

Drinfeld modulepolynomial dynamicsMordell–Lang conjecture

MSC classification

Secondary: 11G09: Drinfel'd modules; higher-dimensional motives, etc. 14K12: Subvarieties 37F10: Polynomials; rational maps; entire and meromorphic functions
Type
Research Article
Information
Compositio Mathematica , Volume 144 , Issue 2 , March 2008 , pp. 304 - 316
Copyright
Copyright © Foundation Compositio Mathematica 2008

References

The second author was partially supported by National Security Agency Grant 06G-067.