Elementary computation of the stable reduction of the Drinfeld modular curve $X(\pi^2)$

Abstract

We compute the stable reduction of the Lubin-Tate space $X(\pi^2)$ in the equal characteristic case, on the basis of Coleman-McMurdy's ideas. Namely, in this paper, we actually construct a stable covering of $X(\pi^2).$ This paper also includes intersection multiplicity datum of the stable model of $X(\pi^2)$. Our method is very explicit and elementary.