Farnell, Shawn, authorPries, Rachel, advisorAchter, Jeffrey D., committee memberPeterson, Christopher Scott, 1963-, committee memberGelfand, Martin Paul, committee member2007-01-032007-01-032010http://hdl.handle.net/10217/44957Let 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.born digitaldoctoral dissertationsengCopyright and other restrictions may apply. User is responsible for compliance with all applicable laws. For information about copyright law, please see https://libguides.colostate.edu/copyright.Artin-SchreiermoduliinvariantdeformationcurveCurves, AlgebraicDeformations of singularitiesModuli theorySmooth affine curvesJacobiansText