On a compactification of a Hurwitz space in the wild case

Let $g$ and $g^{\mathrm{\prime }}$ be two integers and $p$ a prime number. Denote by $\mathscr H_{g, g’, p}^c$themodulispaceofmorphismsofdegree$p$ between smooth curves of genus $g$ and $g^{\mathrm{\prime }}$ and with constant ramification. The purpose of this article is to construct and describe a modular compactification of this space.