I will discuss some new results on the structure of Selmer groups of finite Galois modules over global fields. Tate's definition of the Cassels-Tate pairing can be extended to a pairing on such Selmer groups with little adjustment, and many of the fundamental properties of the Cassels-Tate pairing can be reproved with new methods in this setting. I will also give a general definition of the theta/Mumford group and relate it to the structure of the Cassels-Tate pairing, generalizing work of Poonen and Stoll.

As one application of this theory, I will prove an elementary result on the symmetry of the class group pairing for number fields with many roots of unity and connect this to the work of mine and others on class group statistics.

This work is joint with Adam Morgan.

This talk is part of the online Number Theory Web Seminar, and will be streamed live on Zoom.

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Mike Bennett (University of British Columbia)

Philipp Habegger (University of Basel)

Alina Ostafe (UNSW Sydney)


Alexander Smith

Research Area



Harvard University


Mon, 05/10/2020 - 11:00am


RC-4082, The Red Centre, UNSW