1981/06/01 by Michael Rosen · 1 citation
Mathematics · Computer Science · #Algebraic Geometry and Number Theory #advanced mathematical theories #Polynomial and algebraic computation #Mathematics #Abelian group #Elementary proof #Abelian extension #Extension (predicate logic) #Pure mathematics #Galois group #Class field theory #Kronecker delta #Field (mathematics) #Local field #Genus field #Discrete mathematics #Galois module #Class (philosophy) #Elementary abelian group #Algebra over a field #Geometry
paper · doi:10.2307/1999753
openalex publication_date 1981/06/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/30
Let K be a local field. Lubin and Tate have shown how to explicitly construct an abelian extension of K which they prove to be the maximal abelian extension. Their proof of this result uses local class field theory. When K is a p-adic field we give an elementary proof which even avoids the use of higher ramification groups. Instead we rely on facts about the principal units in a finite abelian extension of K as a module for the Galois group.