Computational Algebra Seminar: Bruin -- Richelot isogenies on Jacobians of genus 2 curves

Speaker: Nils Bruin (Simon Fraser University)
Title: Richelot isogenies on Jacobians of genus 2 curves
Time & Place: 3-4pm, Thursday 9 December, Carslaw 535.

Abstract: Principally polarized abelian surfaces, of which Jacobians of
genus 2 curves are important examples, play an important role in
arithmetic geometry. In some sense, they are "the next step" after
elliptic curves. It is therefore interesting to understand the possible
relations between principally polarized abelian surfaces, which brings us
to the study of isogenies. The simplest case of these (analogous to
2-isogenies on elliptic curves) is that of Richelot isogenies. These are
well-known classically over the complex numbers. I will discuss some of
the complications that arise when one considers more general base fields.

Applications of this more general description of Richelot isogenies
include a complete description of genus 2 curves admitting a degree 4 map
to an elliptic curve.