Equiramified deformations of covers in positive characteristic

Abstract

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

Half of the material from the original version now appears in math.AG/0507274. The main result of the original version has another hypothesis