Results 201 to 210 of about 81,869 (243)
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1986
The abstract class field theory that we have developed in the last chapter is now going to be applied to the case of a local field, i.e., to a field which is complete with respect to a discrete valuation, and which has a finite residue class field. By chap. II, (5.2), these are precisely the finite extensions K of the fields ℚ p or F p ((t)).
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The abstract class field theory that we have developed in the last chapter is now going to be applied to the case of a local field, i.e., to a field which is complete with respect to a discrete valuation, and which has a finite residue class field. By chap. II, (5.2), these are precisely the finite extensions K of the fields ℚ p or F p ((t)).
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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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1979
Standard local class field theory is concerned with complete fields K whose residue field is finite.
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Standard local class field theory is concerned with complete fields K whose residue field is finite.
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Local Class Field Theory: Lubin–Tate Theory
2020This chapter covers local class field theory via Lubin–Tate construction, giving a third proof of the local existence theorem.
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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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1984
By a local field in commutative algebra we mean usually a field of fractions of a complete discrete valuation ring. This notion has many applications in arithmetics and algebraic geometry. In the papers [Usp. Mat. Nauk 30, No. 1 (181), 253--254 (1975; Zbl 0302.14005); Izv. Akad. Nauk SSSR, Ser. Mat.
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By a local field in commutative algebra we mean usually a field of fractions of a complete discrete valuation ring. This notion has many applications in arithmetics and algebraic geometry. In the papers [Usp. Mat. Nauk 30, No. 1 (181), 253--254 (1975; Zbl 0302.14005); Izv. Akad. Nauk SSSR, Ser. Mat.
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Part II Local Class Field Theory
2013Local and global class field theory, as well as a series of further theories for which the name class field theory is similarly justified, have the following principle in common. All of these theories involve a canonical bijective correspondence between the abelian extensions of a field K and certain subgroups of a corresponding module AK associated ...
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Local Class Field Theory: The Reciprocity Map
2020This chapter continues local class field theory with the reciprocity map and existence theorem via Kummer extensions.
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Nuclear effective field theory: Status and perspectives
Reviews of Modern Physics, 2020Hans-Werner Hammer +2 more
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