Higher Class Field Theory in Positive Characteristic

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• Kirsty Syder (University of Nottingham)
• Friday 10 February 2012, 14:00-15:00
• MR3.

If you have a question about this talk, please contact Jonathan Nelson.

Class field theory aims to classify the abelian extensions of a field. Higher class field theory studies the abelian extensions of fields arising from structures in algebraic geometry. The talk begins with a discussion of the basics of classical class field theory, then defines higher local fields, with several basic examples. We will see how to construct a reciprocity map for wildly ramified extensions for higher local fields of positive characteristic using Parshin’s Witt vector pairing, and how this may be applied to the class field theory of schemes over finite fields.

This talk is part of the Junior Algebra and Number Theory seminar series.

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