Gluing curves along their torsion – Jeroen Sijsling

Jeroen Sijsling
Ulm University

Date(s) : 11/02/2021   iCal
11 h 00 min - 12 h 00 min

Let X (resp. Y) be a curve of genus 1 (resp. 2) over a base field k whose characteristic does not equal 2. We give criteria for the existence of a curve Z over k whose Jacobian is up to twist isogenous to the products of the Jacobians of X and Y, and call such a curve a gluing of X and Y.

We also given two methods to determine the curve Z. The first uses interpolation, and also determines the relevant twisting scalar. It can be used to find a Jacobian over QQ that admits a rational 70-torsion point. The second method is more geometrically inspired and exploits the geometry of the Kummer surface of Y.

This is joint work with Jeroen Hanselman and Sam Schiavone.

Meeting ID : 921 9584 8065
Passcode : voir mail
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