CEU Electronic Theses and Dissertations, 2009
| Author | Jossen, Peter Simon |
|---|---|
| Title | On the arithmetic of 1--motives |
| Summary | This thesis deals with arithmetic aspects of 1--motives. We introduce 1--motives with torsion generalizing Deligne's 1--motives and establish arithmetic duality theorems for them, generalizing earlier work of T.Szamuely and D.Harari. We generalize results and techniques developed by J.-P.Serre in his work on the congruence subgroup problem for abelian varieties and a theorem of K.Ribet on Kummer fields associated with abelian varieties over number fields. We also generalize G.Faltings's theorem on homomorphisms of abelian varieties over number fields to 1--motives Combining duality theorems with Kummer theoretic results, we manage to prove that in some interesting cases the Tate--Shafarevich group Scha^2(k,M) of a 1--motive M over a number field k is finite, answering thus partially a question of Harari and Szamuely. Finally, we present an application of our techniques to the problem of ``detecting linear dependence in a Mordell--Weil group''. |
| Supervisor | Szamuely, Tamás |
| Department | Mathematics PhD |
| Full text | https://www.etd.ceu.edu/2009/jossen_peter.pdf |
Visit the CEU Library.
© 2007-2021, Central European University