Automorphisms of hyperelliptic modular curves $X_0(N)$ in positive   characteristic
  We study the automorphism groups of the reduction $X_0(N) \times   \bar{\mathbb{F}}_p$ of a modular curve $X_0(N)$ over primes   $ p\nmid N$. 
Aristides Kontogeorgis, Yifan Yang