Arithmetic properties of curves and Jacobians - Bisogno, Dean M., author; Pries, Rachel, advisor; Achter, Jeffrey, committee member; Cavalieri, Renzo, committee member; Tavani, Daniele, committee member (Colorado State University. Libraries, 2020)
This 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.
Keywords: Galois theory; rational points; Jacobians; curves