whenever a mathematical structure is given in characteristic $p$, one can ask whether it is the reduction, in some sense, of an analogous structure in characteristic zero. if so, the structure in characteristic zero is called a ``lift'' of the structure in characteristic $p$. the most famous example is hensel's lemma about lifting solutions of polynomials in $\mathbb{z}/p$ to solutions in the $p$-adic integers $\mathbb{z}_p$. we will consider a more geometric problem: given a curve $x$ in characteristic $p$ with an action of a finite group $g$, is there a curve in characteristic zero with $g$-action that reduces to $x$? oort conjectured that this could be done when $g$ is cyclic, and his conjecture was recently proven by the speaker, stefan wewers, and florian pop. it turns out that this question reduces to a more ``local'' question about automorphisms of power series rings in one variable. this local question will occupy most of the talk. many examples will be given throughout.