  In this short note, we propose a definition of complete Hurwitz schemes (and
stacks) in mixed characteristic. We follow an idea of R. Pandharipande, and
define the complete Hurwitz stack as a substack of stable maps of degree d of
nodal pointed curves of genus g to the universal curve over the moduli stack of
stable pointed curves of genus h. This substack is simply the closure of the
locus of Hurwitz covers in characteristic 0.
  We describe in detail the reduction modulo 2 of the complete Hurwitz stack of
genus 1 double covers of the projective line. The result is wilder than you
would imagine in your wildest dreams.
  We end by speculating about a possible relationship with the work of
Abramovich-Vistoli about stable maps into Deligne-Mumford stacks.
