Computational Algebra Seminar
We will show how a version of finite descent obstruction for curves is related to a problem on the existence of abelian varieties with prescribed Galois representations. The problem for elliptic curves over the rationals can be solved via Serre's conjecture in the affirmative. We will also discuss some possible counterexamples in other situations.
The canonical height is an important tool in the study of the arithmetic of abelian varieties. We will discuss how the canonical height can be computed in practice in the case of Jacobian varieties and why this is an interesting problem.