Title: Bielliptic Picard curves


Abstract: I'll describe the geometry and arithmetic of the curves y^3 = x^4 + ax^2 + b. The Jacobians of these curves factor as a product of an abelian surface A and an elliptic curve. The surface A is an example of a "false elliptic curve", i.e. it admits quaternionic multiplication.  I'll explain how to see the QM from the geometry of the curve, and then I'll give some results on their groups of rational points A(Q), both torsion and rank. This is based on joint work with Laga and Laga-Schembri-Voight.

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Zoom link
https://huji.zoom.us/j/84721203396?pwd=dWkyVTk0WDhlWlBOdVgxR04rKzM1UT09

Meeting ID: 847 2120 3396
Passcode: 189975

Link to recordings:

https://huji.cloud.panopto.eu/Panopto/Pages/Sessions/List.aspx?folderID=39fd71c4-753c-4a1a-a955-aeb500acd432