Abstract
dc:description.abstractIn this dissertation we study 1-motives over number fields and their application to questions dealing with reductions of points in semiabelian varieties. We prove a version of the Néron-Ogg-Shafarevich criterion for 1-motives and show how the image of the Frobenius in the ℓ-adic Galois representation associated to a 1-motive determines the ℓ-part of its reduction modulo the corresponding prime. We use this theory to investigate a family of properties for points in tori which we call algebraic dependences. In particular, we study the rank of the reduction of a group generated by two rational points in G2m, modulo different primes. Finally, we show how our algebraic dependences exhibit an analogy between problems in p-adic transcendence theory and problems concerning reduction of points.
Degree
thesis:*- Level thesis:degree_level
- thesis.doctoral
- Grantor dc:publisher
- Universität Bayreuth
- Year
- 2013
Author and committee
dc:creator, dc:contributor.*- Author dc:creator
-
- Matev, Tzanko
- Contributors dc:contributor
-
- Stoll, Michael
Identifiers
dc:identifier.*- Repository record source_url
- https://epub.uni-bayreuth.de/id/eprint/1721/
- OAI identifier oai:identifier
- oai:epub.uni-bayreuth.de:1721