Unramified class field theory for orders
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- by Peter Stevenhagen PDF
- Trans. Amer. Math. Soc. 311 (1989), 483-500 Request permission
Abstract:
The main theorem of unramified class field theory, which states that the class group of the ring of integers of a number field $K$, is canonically isomorphic to the Galois group of the maximal totally unramified abelian extension of $K$ over $K$, is generalized and proved for all infinite commutative rings with unit that, like rings of integers, are connected and finitely generated as a module over ${\mathbf {Z}}$. Modulo their nilradical, these rings are exactly the connected orders in products of number fields.References
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Additional Information
- © Copyright 1989 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 311 (1989), 483-500
- MSC: Primary 11R37; Secondary 11R54
- DOI: https://doi.org/10.1090/S0002-9947-1989-0978366-3
- MathSciNet review: 978366