
## 9. At what level do we see deformation?

1. #### Problem 9.1.

[Boston] Is there a deformation theory for arboreal Galois representations?
1. 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 p-adic 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.