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- Selmer groups and a Cassels-Tate pairing for finite Galois modules
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- Home
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Postgraduate research
- Info for new students
- Current research students
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- Michael Tallis PhD Research Travel Award
- Information about research theses
- Past research students
- Resources
- Entry requirements
- PhD projects
- Obtaining funding
- Application & fee information
Student services
- Help for postgraduate students
- Thesis guidelines
- School assessment policies
- Computing information
- Mathematics Drop-in Centre
- Consultation
- Statistics Consultation Service
- Academic advice
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Abstract:
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.
To attend the talks, registration is necessary. To register please visit our website
Registered users will receive an email before each talk with a link to the Zoom meeting.
Organisers:
Mike Bennett (University of British Columbia)
Philipp Habegger (University of Basel)
Alina Ostafe (UNSW Sydney)