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A case of the dynamical Mordell-Lang conjecture
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).ORCID iD: 0000-0003-4734-5092
2012 (English)In: Mathematische Annalen, ISSN 0025-5831, E-ISSN 1432-1807, Vol. 352, no 1, 1-26 p.Article in journal (Refereed) Published
Abstract [en]

We prove a special case of a dynamical analogue of the classical Mordell- Lang conjecture. Specifically, let phi be a rational function with no periodic critical points other than those that are totally invariant, and consider the diagonal action of phi on (P(1))(g). If the coefficients of phi are algebraic, we show that the orbit of a point outside the union of the proper preperiodic subvarieties of (P(1))(g) has only finite intersection with any curve contained in (P(1))(g). We also show that our result holds for indecomposable polynomials phi with coefficients in C. Our proof uses results from p-adic dynamics together with an integrality argument. The extension to polynomials defined over C uses the method of specialization coupled with some new results of Medvedev and Scanlon for describing the periodic plane curves under the action of (phi, phi) on A(2).

Place, publisher, year, edition, pages
Springer, 2012. Vol. 352, no 1, 1-26 p.
Keyword [en]
RATIONAL FUNCTIONS; POINTS; VARIETIES; EQUATIONS; CURVES; MAPS
National Category
Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-70026DOI: 10.1007/s00208-010-0621-4ISI: 000298649800001Scopus ID: 2-s2.0-84855219337OAI: oai:DiVA.org:kth-70026DiVA: diva2:485817
Note
QC 20120130Available from: 2012-01-30 Created: 2012-01-30 Last updated: 2017-12-08Bibliographically approved

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Kurlberg, Pär

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