Transcription of Class Field Theory - James Milne
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Class Field Theory - James Milne
Class Field MilneVersion 23, 2013 Class Field Theory describes the abelian extensions of a local or global Field in terms of thearithmetic of the Field itself. These notes contain an exposition of abelian Class Field theoryusing the algebraic/cohomological approach of Chevalley and Artin and Tate. The explicitapproach of Lubin and Tate in the local case and the analytic approach in the global caseare also explained. The original version of the notes was distributed during the teaching ofan advanced graduate Milne },title={ Class Field Theory ( )},year={2013},note={Available at },pages={281+viii}} (August 14, 1996). First version on the (May 6, 1997). Substantially revised and expanded; 222 (March 2, 2008). Corrected, revised, and expanded; 287 (May 30, 2011). Many minor fixes; 287 (March 23, 2013). Minor fixes and improvements; 289 at send comments and corrections to me at the address on my web photograph is of Mt Christina from the McKellar Saddle, New 1996, 1997, 2008, 2011, 2013, paper copies for noncommercial personal use may be made without explicit permis-sion from the copyright Class Field Theory : Lubin-Tate Theory191 Statements of the Main Theorems.
Introduced Hecke L-series generalizing both Dirichlet’s L-series and Dedekind’s zeta functions. ARTIN (1898–1962). He found the “Artin reciprocity law”, which is the main theorem of class field theory (improvement of Takagi’s results). Introduced the Artin L-series. HASSE (1898–1979). He gave the first proof of local class ...
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