On algebraic curves in prime characteristic

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

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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
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

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