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Friday, October 9, 2015

1:10 PM - 2:00 PM (ET)

Exley Science Center (Tower)

Event Type

Seminar/Colloquium

Contact

Christopher Rasmussen

Department

Mathematics and Computer Science

Link

https://eaglet.wesleyan.edu/MasterCalendar/EventDetails.aspx?EventDetailId=64663

** Abstract**:
The classification of the torsion
subgroup of elliptic curves over \mathbb{Q} was determined by Mazur. The
classification over quadratic number fields was completed due to work of
Kamienny, Kenku, and Momose.

However, over cubic fields the classification is already incomplete. In this talk we discuss a refined version of this problem: let E be an elliptic curve defined over \mathbb{Q} and K be a number field of degree d; what groups appear as E(K)_{\text{tors}}? In particular, we will present a classification over all quartic Galois number fields K and show how the techniques used may be applied to other fields.