On ramification theory in the imperfect residue field case
- St. Petersburg State University, St. Petersburg (Russian Federation)
This paper is devoted to the ramification theory of complete discrete valuation fields such that the residue field has prime characteristic p and the cardinality of a p-base is 1. This class contains two-dimensional local and local-global fields. A new definition of ramification filtration for such fields is given. It turns out that Hasse-Herbrand type functions can be defined with all the usual properties. Thanks to this, a theory of upper ramification groups and the ramification theory of infinite extensions can be developed. The case of two-dimensional local fields of equal characteristic is studied in detail. A filtration on the second K-group of the field in question is introduced that is different from the one induced by the standard filtration on the multiplicative group. The reciprocity map of two-dimensional local class field theory is proved to identify this filtration with the ramification filtration.
- OSTI ID:
- 21208369
- Journal Information:
- Sbornik. Mathematics, Vol. 194, Issue 12; Other Information: DOI: 10.1070/SM2003v194n12ABEH000785; Country of input: International Atomic Energy Agency (IAEA); ISSN 1064-5616
- Country of Publication:
- United States
- Language:
- English
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