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MT Research Seminar: Preperiodic portraits modul primes March 18, 2014 (11:00 AM PDT - 12:30 PM PDT)
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Location: MSRI: Simons Auditorium
Speaker(s) Thomas Tucker (University of Rochester)
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Let  F be a rational function of degree > 1 over a  number field or function field K and let z be a point that is not preperiodic.   Ingram and Silverman conjecture that for all but finitely many positive integers (m,n), there is a prime p such that z has exact preperiodic m and exact period n (we call this pair (m,n) the portrait of z modulo p).

  We present some counterexamples to this conjecture and show that a generalized form of abc implies -- one that is true for function fields -- implies  that these are the only counterexamples.  We also present  a connection with Douady-Thursto-Hubbard rigidity.  This represents joint work with several authors.

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