School of Mathematics and Statistics
Number Theory Seminar 

In this introductory talk, Sschemes are defined as we attempt to understand the three most relavent properties of Sschemes (regular, smooth and proper) by providing intuitive examples. From this we will see the hurdles in obtaining a smooth group scheme whose generic fibre is an elliptic curve. This leads to the study of Néron models (smooth group schemes which have this property, assuming they exist!), and will be looked at in more detail next week. 