Bisogno, Dean M., authorPries, Rachel, advisorAchter, Jeffrey, committee memberCavalieri, Renzo, committee memberTavani, Daniele, committee member2021-01-112021-01-112020https://hdl.handle.net/10217/219607This thesis is about algebraic curves and their Jacobians. The first chapter concerns Abhyankar's Inertia Conjecture which is about the existence of unramified covers of the affine line in positive characteristic with prescribed ramification behavior. The second chapter demonstrates the existence of a curve C for which a particular algebraic cycle, called the Ceresa cycle, is torsion in the Jacobian variety of C. The final chapter is a study of supersingular Hurwitz curves in positive characteristic.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.Galois theoryrational pointsJacobianscurvesText