Independent Studies in Class Field Theory — CFT

  • Instructor: Gergely Zábrádi
  • Contact: g.zabradi at g mail dot com
  • Prerequisites: abstract algebra: a solid background in the field of abstract algebra (groups, rings, modules, Galois theory); introductory algebraic number theory (ideal class group, ramification theory, local fields); some knowledge of cohomology (either topology/geometry/algebra) is an advantage, but not necessary.
  • Text: Neukirch: Class field theory

Course description: This reading course provides an introduction to class field theory. Students are expected to read through, with consultation, the first two parts of Neukirch's book `Class field theory' (covering group cohomology and local class field theory).

Topics:

    group cohomology; long exact sequence; inflation, restriction, corestriction; cup product; Tate cohomology; abstract class field theory; Galois cohomology; multiplicative group of local fields; class formation; local reciprocity law; existence theorem of local class field theory.

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