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5. Boundary of $M_d$


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      Problem 5.1.

      [Rachel Pries] Give an algebraic description of the boundary and maps in the boundary in characteristic $p$ not necessarily $0.$ (Reference DeMarco). Try $d=3.$ Motivation: results for moduli curves use understanding of the boundary.


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          Problem 5.2.

          [Holly Krieger]
          1. (Want to look at a curve in $M_2$). For $f(z)=\frac{z^2-1}{z^2-c},$ there is a collection of PCF maps which approach $c=1$ on the curve. Compare the arboreal representation for $f$ to the representation of the limit map.
          2. More generally, how do these representations behave as you deform to the boundary?

              Cite this as: AimPL: The Galois theory of orbits in arithmetic dynamics, available at http://aimpl.org/galarithdyn.