Uniformization of Elliptic Curves

                                                                                        Özge Ülkem
                                                                                Mathematics, MSc. Thesis, 2015

Thesis Jury

Prof. Dr. Henning Stichtenoth(Thesis Advisor), Assoc. Prof. Alp Bassa( Thesis Co-advisor), Prof. Dr. Alev Topuzoğlu, Assoc. Prof. Cem Güneri, Assoc. Prof. Özgür Gürbüz

Date & Time: 4th, August 2015 –  3.00 AM

Place: FENS L062

Keywords : Elliptic curve, Uniformization, Tate curve

Abstract

It is known that each lattice in complex numbers defines an elliptic curve via Weierstass function. This gives us an injection between the set of lattices- up to homothehy- and the set of elliptic curves, up to isomorphism. In fact, this injection is a bijection, which is called uniformization of elliptic curves over comlex numbers. Later on, John Tate showed that this is true also for elliptic curves over a p-adic field. In this thesis, I describe Tate’s theory  and derive a uniformization of elliptic curves over a p-adic field.