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Class Field Theory for Arithmetic Surfaces
K-Theory, 1998Let \(k\) be an algebraic number field, \(X\) a smooth projective curve over \(k\) and \(Y\) a regular proper flat model of \(X\) over the ring of integers of \(k\). Take an effective reduced divisor \(D\) on \(X\) and its closure \(\overline D\) on \(Y\).
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The Structure of Local Class Field Theory
American Journal of Mathematics, 1938Ist für einen diskret-bewerteten perfekten Körper \(k\) der Restklassenkörper \(\mathfrak k\) endlich, so gelten die bekannten Sätze der lokalen Klassenkörpertheorie über \(k\): Für jedes \(n\) gibt es genau einen unverzweigten Erweiterungskörper vom Grade \(n\) über \(k\), und dieser ist zyklisch.
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Idele-Class Factor Sets and Class Field Theory
The Annals of Mathematics, 1952requirements. His construction starts with the factor set obtained from the class field theory and yields the desired one in RK as the result of an analysis of the cohomology structure of TK, among others. In the present paper, we wish to propose a direct construction which leads to the same factor set (whence to the same extension group).
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Cohomology in Class Field Theory
The Annals of Mathematics, 1952Hochschild, G., Nakayama, T.
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Class Field Theory. Field Extensions
1971In this brief survey on class field theory and related questions we mainly present the papers reviewed in the “Mathematics” section of Referativnyi Zhurnal during 1958–1967. Among the books published during this time we note those by Chevalley [20] (a systematic exposition and application of cohomology groups), Artin and Tate [12] (the most modern ...
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1986
The role held in local class field theory by the multiplicative group of the base field is taken in global class field theory by the idele class group. The notion of idele is a modification of the notion of ideal. It was introduced by the French mathematician Claude Chevalley (1909–1984) with a view to providing a suitable basis for the important local-
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The role held in local class field theory by the multiplicative group of the base field is taken in global class field theory by the idele class group. The notion of idele is a modification of the notion of ideal. It was introduced by the French mathematician Claude Chevalley (1909–1984) with a view to providing a suitable basis for the important local-
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1985
L'article est la première partie d'une ouvrage qui a comme but un exposé detailé du mémoire de \textit{M. Hazewinkel}: ''Local class field theory is easy'', Adv. Math. 18, 148--181 (1975; Zbl 0312.12022).
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L'article est la première partie d'une ouvrage qui a comme but un exposé detailé du mémoire de \textit{M. Hazewinkel}: ''Local class field theory is easy'', Adv. Math. 18, 148--181 (1975; Zbl 0312.12022).
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