THE DRINFELD MODULAR INTERPRETATION OF AN ASYMPTOTICALLY

OPTIMAL TOWER OF CURVES CONSTRUCTED BY A. GARCIA AND H. STICHTENOTH

Türkü Özlüm Çelik
Mathematics, MSc. Thesis 2014

Thesis Jury

Assoc. Prof. Cem Güneri (Thesis Advisor), Assoc. Prof. Alp Bassa (Thesis Co-Advisor),

Prof. Dr. Henning Stichtehoth, Prof. Dr. Alev Topuzoğlu,

Assoc. Prof. Hüsnü Yenigün 

Date & Time: 9th December, 2014 –  18:00

Place: Sabancı University, FENS 1040

Keywords : Drinfeld Modular Curves

Abstract

I study on Drinfeld modular interpretation of maximal curves that are curves that attain Hasse-Weil bound. This bound is an immediate consequence of the Riemann Hypothesis for zeta functions associated to curves over finite fields, which has been proven and is known as the Hasse--Weil theorem. The Hermitian curve (also called the Fermat curve) is a famous maximal one. It is also known that all subcovers of the Hermitian curve are maximal due to a theorem of Serre. Noam D. Elkies recovered the Hermitian curve as the reduction of a Drinfeld modular curve. In this thesis I focus on that work of Noam. D. Elkies.