1. Kummer theory for commutative algebraic groups
- Author
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Tronto, Sebastiano, Stevenhagen, P., Bruin, P.J., Perucca, A., Fiocco, M., Luijk, R.M. van, Voight, J., Wiese, G., Salgado Guimaraes da Silva, C., Leiden University, Perucca, Antonella [superviser], Bruin, Peter J. [superviser], Wiese, Gabor [president of the jury], Lenstra, Hendrik [member of the jury], Salgado Guimarães da Silva, Cecília [member of the jury], and Taelman, Lenny [member of the jury]
- Subjects
Field extensions ,torsion fields ,Algebraic curves ,Galois representations ,Cyclotomic fields ,algebraic groups ,Torsion fields ,Number theory ,elliptic curves ,Mathematics [G03] [Physical, chemical, mathematical & earth Sciences] ,Elliptic curves ,cyclotomic fields ,Mathématiques [G03] [Physique, chimie, mathématiques & sciences de la terre] ,Kummer theory - Abstract
This dissertation is a collection of four research articles devoted tothe study of Kummer theory for commutative algebraic groups. In numbertheory, Kummer theory refers to the study of field extensions generatedby n-th roots of some base field. Its generalization to commutativealgebraic groups involves fields generated by the division points of afixed algebraic group, such as an elliptic curve or a higher dimensionalabelian variety. Of particular interest in this dissertation is the degreeof such field extensions. In the first two chapter, classical results forelliptic curves are improved by providing explicitly computable bounds anduniform and explicit bounds over the field of rational numbers. In thelast two chapters a general framework for the study of similar problemsis developed.
- Published
- 2022