|Title: Genus one curves in Severi-Brauer Varieties.|
|Speaker: David Saltman of IDA|
|Contact: David Zureick-Brown, firstname.lastname@example.org|
|Date: 2016-03-15 at 5:00PM|
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 \subset 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.
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