Last modified date: <%+ tp.file.last_modified_date() %>

• Tags
  • #NT/algebraic
• Refs:
  • https://ocw.mit.edu/courses/mathematics/18-786-number-theory-ii-class-field-theory-spring-2016/lecture-notes
  • https://www3.nd.edu/~ajorza/courses/2014s-m80220/notes/lecture26.pdf
  • http://math.uchicago.edu/~may/REU2014/REUPapers/Lingle.pdf
  • Notes on absolute Galois groups: attachments/Absolute Galois Groups.pdf
  • https://pub.math.leidenuniv.nl/~smitbde/edu/lcft_2011/index.php?menu=schedule
  • Juvitop 2021 notes: attachments/Juvitop_CFT_Notes.pdf
  • Brief summary of main statements: http://www-math.mit.edu/~poonen/papers/cft.pdf #resources/summaries
  • https://kskedlaya.org/cft/preface-1.html
    • https://math.ucsd.edu/~kkedlaya/math204b/
• Links:
  • Local class field theory
  • Global class field theory
  • Artin map
  • ray class
  • Artin reciprocity
  • Unsorted/Dedekind-Kummer theorem
  • Lubin-Tate

class field theory

What is a class field?

See class group, fractional ideal, Galois module, totally unramified extension, Artin map.

Local class field theory

See profinite completion.

Global Class Field Theory

Results

• There is a correspondence between Hecke characters and representations of abelian Galois groups. # Notes

- Class field theory is Langlands for \(\operatorname{GL}_1\). - Pasted image 20211105234852.png - Pasted image 20211105235549.png - Pasted image 20211106001614.png