Lifting Problem on Automorphism Groups of Cyclic Curves
  Let X be a smooth projective hyperelliptic curve over an algeraically closed field k of prime characteristic p. The aim of this note is to find necessary and sufficient conditions on the automorphism group of the curve X to be lifted to characteristic zero. The results will be generalised for a certain family of curves that we call cyclic curves. 
Tovondrainy Christalin Razafindramahatsiaro
math.AG