Uniformization of Elliptic Curves
Mathematics, MSc. Thesis, 2015
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
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.