A generalization of class formation by using hypercohomology (Q1174955)
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scientific article; zbMATH DE number 9803
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A generalization of class formation by using hypercohomology |
scientific article; zbMATH DE number 9803 |
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A generalization of class formation by using hypercohomology (English)
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25 June 1992
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The author reproves the isomorphism theorem of class field theory for two-dimensional local fields [\textit{A. N. Parshin}, Usp. Mat. Nauk 30, No. 1(181), 253-254 (1975; Zbl 0302.14005); \textit{K. Kato}, J. Fac. Sci., Univ. Tokyo, Sect. IA 27, 603-683 (1980; Zbl 0463.12006)]. He defines the notion of class formations for bounded complexes of \(G\)-modules, where \(G\) is a profinite group and proves a generalization of the Tate-Nakayama theorem. For the proof of the isomorphism theorem he uses facts about Lichtenbaum's complex \(\mathbb{Z}(2)\) which are partially published only as Preprint in 1988.
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complete discrete valuation fields
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isomorphism theorem
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class field
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two-dimensional local fields
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class formations
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Tate-Nakayama theorem
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0.86850864
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0.8573699
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0.85702455
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