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Galois Seminar

Friday, March 3, 2017 - 3:15pm

Mirela Ciperiani

IAS Princeton & UT Austin


University of Pennsylvania


Tea will be served at 3:00 PM in the Math Lounge, DRL 4th floor

Genus one curves with a fixed Jacobian can be viewed as elements of the Weil-Chatelet group.  We will discuss divisibility questions within this group. This leads us to analyzing the divisibility properties of the Tate-Shafarevich group.  There are two related questions:

1. Are the elements of the Tate-Shafarevich group divisible within the Weil-Chatelet group? (Cassels' question.)

2. How does the Tate-Shafarevich group intersect the maximal divisible subgroup of the Weil-Chatelet group? (Bashmakov's question.)

We will discuss our answers to these questions. This is joint work with Jakob Stix (Univ of Frankfurt).