The Dynamical Mordell-Lang Conjecture predicts the structure of the intersection between a subvariety VV of a variety XX defined over a field KK of characteristic 00 with the orbit of a point in X(K)X(K) under an endomorphism ΦΦ of XX. The Zariski dense conjecture provides a dichotomy for any rational self-map ΦΦ of a variety XX defined over an algebraically closed field KK of characteristic 00: either there exists a point in X(K)X(K) with a well-defined Zariski dense orbit, or ΦΦ leaves invariant some non-constant rational function ff. For each one of these two conjectures we formulate an analogue in characteristic pp; in both cases, the presence of the Frobenius endomorphism in the case XX is isotrivial creates significant complications which we will explain in the case of algebraic tori.
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Mike Bennett (University of British Columbia)
Philipp Habegger (University of Basel)
Alina Ostafe (UNSW Sydney)
Number Theory Seminar
University of British Columbia
Tue, 01/12/2020 - 12:00pm
RC-4082, The Red Centre, UNSW