Universiteit Leiden

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Groups and fields in arithmetic

Promotor: Prof.dr. H.W. Lenstra

M.F. Kosters
04 juni 2014
Thesis in Leiden Repository

This thesis consists of 8 chapters in which we discuss various aspects of arithmetic. In the first chapter, we give an introduction to the algebraic theory of valued fields. In the second chapter, we give an introduction to the theory of normal projective curves. In particular, we study curves over finite fields. In the third and fourth chapters, we study images of maps between curves over large fields and over finite fields. In the fifth chapter, we study the subset sum problem for finite abelian groups. In the sixth and seventh chapters, we discuss how to obtain generators for the Picard group of a hyperelliptic curve over a finite field in a deterministic way. In the last chapter, we study automorphism groups of field extensions which are not necessarily algebraic.