Two problems in the theory of curves over fields of positive characteristic

Hong, Euijin

Permalink

https://hdl.handle.net/2142/104786 Copy

Description

Title

Two problems in the theory of curves over fields of positive characteristic

Author(s)

Hong, Euijin

Issue Date

2019-04-17

Director of Research (if dissertation) or Advisor (if thesis)

• Haboush, William
• Duursma, Iwan

Doctoral Committee Chair(s)

Katz, Sheldon

Committee Member(s)

Dodd, Christoper

Department of Study

Mathematics

Discipline

Mathematics

Degree Granting Institution

University of Illinois at Urbana-Champaign

Degree Name

Ph.D.

Degree Level

Dissertation

Keyword(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.

Graduation Semester

2019-05

Type of Resource

text

Permalink

http://hdl.handle.net/2142/104786

Copyright and License Information

⃝c 2019 by Euijin Hong. All rights reserved.

Owning Collections