Type: Seminar

Distribution: World

Expiry: 9 Dec 2010

Auth: billu@daumier.maths.usyd.edu.au

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.