Computational Algebra Seminar: Voloch, Mueller

Speaker: Felipe Voloch (University of Texas)
Title: Finite descent obstruction and modularity
Time & Place: 3:05-3:55pm, Thursday 10 March, Carslaw 535

Abstract: 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.

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Speaker: Jan Steffen Mueller (Bayreuth)
Title: Computing canonical heights on Jacobians
Time & Place: 4:05-4:55pm, Thursday 10 March, Carslaw 535

Abstract: 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.