Explicit constructions of asymptotically good towers of function fields

Abstract

In this thesis the theory required to construct and analyse the asymptotic behaviour of explicit towers of function fields is developed. Various towers are exhibited, and general families of explicit formulae for which the splitting behaviour and growth of the genus can be computed in a tower are discussed. When the necessary theory has been developed, the focus is on the case of towers over fields of non-square cardinality and the open problem of how good the asymptotic behaviour of the tower is under these circumstances.