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Effective bounds on S-integral preperiodic points for polynomials

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If you have a question about this talk, please contact Rong Zhou.

Through an analogy between torsion points on abelian varieties, and preperiodic points (points which eventually enter a cycle under iteration) of rational functions, problems in unlikely intersections motivated S. Ih to conjecture the finiteness of preperiodic points for a rational function on P^1, defined over a number field, which satisfy a certain integrality condition.

This conjecture remains open, and has only been proved (a) in the case very special maps, and (b) under certain local conditions. I will discuss how to obtain effective results in the latter context (following work of Petsche), and how to compute explicit bounds in the case of a unicritical polynomial.

This talk is part of the Number Theory Seminar series.

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