Selmer groups and a Cassels-Tate pairing for finite Galois modules

Selmer groups and a Cassels-Tate pairing for finite Galois modules

-
Alexander Smith, Massachusetts Institute of Technology

Zoom link:  https://princeton.zoom.us/j/97126136441

Passcodethe three digit integer that is the cube of the sum of its digits

 

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.