Hurwitz trees and deformations of Artin-Schreier covers

The main focus of this thesis is equal characteristics deformations of Artin-Schreier covers (of curves). We formulate some conditions on a combinatorial object called Hurwitz tree to determine the existence of certain types of deformations of given degree p cyclic branched covers. Furthermore, by applying these Hurwitz tree criteria, we show that the moduli space of Artin-Schreier curves of fixed genus is connected when the genus is sufficiently large.