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A Note on Class Field Theory for Two-Dimensional Local Rings

Published online by Cambridge University Press:  04 December 2007

Atsushi Shiho
Atsushi Shiho
Affiliation:
Mathematical Institute, Tohoku University, Aoba-ku, Sendai 980-8578, Japan. E-mail: [email protected]
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Abstract

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The class field theory for the fraction field of a two-dimensional complete normal local ring with finite residue field is established by S. Saito. In this paper, we investigate the index of the norm group in the K2-idele class group for a finite Abelian extension of such fields and deduce that the existence theorem does not hold for almost fields in this case.

Keywords

class field theorytwo-dimensional local ringindex of norm groupexistence theoremtwo-dimensional Abelian covering singularity
Type
Research Article
Information
Compositio Mathematica , Volume 124 , Issue 3 , December 2000 , pp. 305 - 340
Copyright
© 2000 Kluwer Academic Publishers