Equiramified deformations of covers in positive characteristic

Suppose $\varphi$ is a wildly ramified cover of germs of curves defined over an algebraically closed field of characteristic p. We study unobstructed deformations of $\varphi$ in equal characteristic, which are equiramified in that the branch locus is constant and the ramification filtration is fixed. We show that the moduli space $M_{\varphi }$ parametrizing equiramified deformations of $\varphi$ is a subscheme of an explicitly constructed scheme. This allows us to give an explicit upper and lower bound for the Krull dimension $d_{\varphi }$ of $M_{\varphi }$. These bounds depend only on the ramification filtration of $\varphi$. When $\varphi$ is an abelian p-group cover, we use class field theory to show that the upper bound for $d_{\varphi }$ is realized.