9. At what level do we see deformation?

Problem 9.1.
[Boston] Is there a deformation theory for arboreal Galois representations?
Remark. Consider $x^2+t$ where $t^2=0$ over Artinian ring $K[t]/t^2$ or $K[t]/t^n$ for $n\geq 1.$

Remark. [Boston] Can we parametrize arboreal Galois representations as we do padic Galois representations? This is different from the direction of the other remark.


Problem 9.2.
To what level can the representation associated to two quadratic polynomials agree?
Cite this as: AimPL: The Galois theory of orbits in arithmetic dynamics, available at http://aimpl.org/galarithdyn.