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A Note on Class Field Theory for Two-Dimensional Local Rings |
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| Authors: | Atsushi Shiho |
| Institution: | (1) Mathematical Institute, Tohoku University, Aoba-ku, Sendai, 980-8578, Japan |
| Abstract: | 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 K 2-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 theory two-dimensional local ring index of norm group existence theorem two-dimensional Abelian covering singularity |
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