Artin-Schreier curves - Farnell, Shawn, author; Pries, Rachel, advisor; Achter, Jeffrey D., committee member; Peterson, Christopher Scott, 1963-, committee member; Gelfand, Martin Paul, committee member (Colorado State University. Libraries, 2010)
Let k be an algebraically closed field of characteristic p where p is a prime number. The main focus of this work is on properties of Artin-Schreier curves. In particular, we study two invariants of the p-torsion of the Jacobian of these curves: the p-rank and the a-number. In the main result, we demonstrate a family of Artin-Schreier curves for which the a-number is constant. We also give a result concerning the existence of deformations of Artin-Schreier curves with varying p-rank.
Keywords: Artin-Schreier; moduli; invariant; deformation; curve; Curves, Algebraic; Deformations of singularities; Moduli theory; Smooth affine curves; Jacobians