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Description
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 |
This item appears in the following Collection(s)
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Dissertations and Theses - Mathematics
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Graduate Dissertations and Theses at Illinois
Graduate Theses and Dissertations at Illinois