Artin-Schreier curves
Date
2010
Authors
Farnell, Shawn, author
Pries, Rachel, advisor
Achter, Jeffrey D., committee member
Peterson, Christopher Scott, 1963-, committee member
Gelfand, Martin Paul, committee member
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Journal ISSN
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Abstract
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.
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Subject
Artin-Schreier
Curves, Algebraic
moduli
Deformations of singularities
invariant
Moduli theory
deformation
Smooth affine curves
curve
Jacobians