Anbar, Nurdagül
(2012)
*On algebraic curves in prime characteristic.*
[Thesis]

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Official URL: http://192.168.1.20/record=b1499102 (Table of Contents)

## Abstract

In this thesis we consider two problems related to algebraic curves in prime characteristic. In the first part, we study curves defined over the finite field Fq. We prove that for each sufficiently large integer g there exists a curve of genus g with prescribed number of degree r points for r = 1,..., m. This leads to the existence of a curve whose L-polynomial has prescribed coefficients up to some degree. In the second part, we consider curves defined over algebraically closed fields K of odd characteristic. We show that a plane smooth curve which has a K-automorphism group of order larger than 3(2g2 + g)([square root]8g + 1 + 3) must be birationally equivalent to a Hermitian curve.

Item Type: | Thesis |
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Uncontrolled Keywords: | Artin-schreier extension. -- Sutomorphism. -- Curve. -- Degree r point. -- Function field. -- Hurwitz genus formula. -- Order sequence. -- Artin-Schreier genişlemesi. -- Otomorfizma. -- Eğri. -- Derecesi r olan nokta. -- Fonksiyonel cisimler. -- Hurwitz cins formülü. -- Derece dizisi. |

Subjects: | Q Science > QA Mathematics |

Divisions: | Faculty of Engineering and Natural Sciences > Basic Sciences > Mathematics Faculty of Engineering and Natural Sciences |

Depositing User: | IC-Cataloging |

Date Deposited: | 20 Dec 2014 13:56 |

Last Modified: | 26 Apr 2022 10:03 |

URI: | https://research.sabanciuniv.edu/id/eprint/26551 |