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SUMMARY:Dragos Ghioca (University of British Columbia)
DTSTART:20201111T190000Z
DTEND:20201111T195000Z
DTSTAMP:20260422T220758Z
UID:20w5206/7
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/20w5206/7/">
 A couple of conjectures in arithmetic dynamics over fields of positive cha
 racteristic</a>\nby Dragos Ghioca (University of British Columbia) as part
  of BIRS workshop: Algebraic Dynamics and its Connections to Difference an
 d Differential Equations\n\n\nAbstract\nThe Dynamical Mordell-Lang Conject
 ure predicts the structure of the intersection between a subvariety $V$ of
  a variety $X$ defined over a field $K$ of characteristic $0$ with the orb
 it of a point in $X(K)$ under an endomorphism $\\Phi$ of $X$. The Zariski 
 dense conjecture provides a dichotomy for any rational self-map $\\Phi$ of
  a variety $X$ defined over an algebraically closed field $K$ of character
 istic $0$: either there exists a point in $X(K)$ with a well-defined Zaris
 ki dense orbit\, or $\\Phi$ leaves invariant some non-constant rational fu
 nction $f$. For each one of these two conjectures we formulate an analogue
  in characteristic $p$\; in both cases\, the presence of the Frobenius end
 omorphism in the case $X$ is isotrivial creates significant complications 
 which we will explain in the case of algebraic tori.\n
LOCATION:https://researchseminars.org/talk/20w5206/7/
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