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Title:Two problems in the theory of curves over fields of positive characteristic
Author(s):Hong, Euijin
Director of Research:Haboush, William; Duursma, Iwan
Doctoral Committee Chair(s):Katz, Sheldon
Doctoral Committee Member(s):Dodd, Christoper
Department / Program:Mathematics
Discipline:Mathematics
Degree Granting Institution:University of Illinois at Urbana-Champaign
Degree:Ph.D.
Genre:Dissertation
Subject(s):Algebraic Geometry
Algebraic Geometry Code
Abstract:This thesis consists of two parts. In the first half, we define, so called, generalized Artin-Schreier cover of a scheme X over k. After defining Artin-Schreier group scheme Γ over X, a generalized Artin-Schreier cover is realized as a principal homogeneous space of Γ. We are especially interested in the case when X is P1\{0,1,∞}, a thrice punctured plane. An argument of (generalized) Artin-Schreier field extension and its function field arithmetic follows. The second half is about the coding theory. For a full flag of codes, if it is equivalent to its duals, then it is said to have the isometry-dual property. Introducing characterizations of isometry-dual property for one-point AG codes and its preservation after puncturing at some points, some generalizations in different directions will be given.
Issue Date:2019-04-17
Type:Text
URI:http://hdl.handle.net/2142/104786
Rights Information:⃝c 2019 by Euijin Hong. All rights reserved.
Date Available in IDEALS:2019-08-23
Date Deposited:2019-05


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