Selmer groups and a听Cassels-Tate pairing for finite Galois modules
Selmer groups and a听Cassels-Tate pairing for finite Galois modules
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Alexander Smith, Massachusetts Institute of Technology
Zoom link:听听
Passcode:听the three digit integer that is the cube of the sum of its digits
听
I will discuss some new results听on the structure of Selmer groups of finite Galois modules over global fields. Tate's definition of the听Cassels-Tate pairing can be extended to a pairing on such Selmer groups with little adjustment, and many of the fundamental properties of the听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听Cassels-Tate pairing, generalizing work of Poonen and Stoll.