Algebraic Geometry Seminar

Genus One Curves in Severi-Brauer Varieties

Speaker: David Saltman, Center for Communications Research, IDA

Location: Warren Weaver Hall 1302

Date: Tuesday, March 29, 2016, 2 p.m.


Let A/F be a division algebra of degree 3, and X its Severi-Brauer variety which is a form of the projective plane. The linear system of cubic curves is defined on X, and so we can let C in X be one such. If C is a nonsingular such curve, then C is a genus one curve with Jacobian E, an elliptic curve. The question we address is the one asked by Asher Auel, namely, which E arise. We give an answer that depends on the structure of A.