Results 281 to 290 of about 2,507,409 (326)
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2003
Global class field theory is a major achievement of algebraic number theory, based on the Artin reciprocity map and the existence theorem. The author works out the consequences and the practical use of these results by giving detailed studies and illustrations of classical subjects (classes, idèles, ray class fields, symbols, reciprocity laws, Hasse's ...
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Global class field theory is a major achievement of algebraic number theory, based on the Artin reciprocity map and the existence theorem. The author works out the consequences and the practical use of these results by giving detailed studies and illustrations of classical subjects (classes, idèles, ray class fields, symbols, reciprocity laws, Hasse's ...
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1997
There are two main problems in the theory of algebraic number fields: On the one hand the description of the arithmetical properties of a given number field and on the other hand the description of number fields with given arithmetical properties.
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There are two main problems in the theory of algebraic number fields: On the one hand the description of the arithmetical properties of a given number field and on the other hand the description of number fields with given arithmetical properties.
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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 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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1999
Every field k is equipped with a distinguished Galois extension: the separable closure \(\bar k|k\). Its Galois group \({G_k} = G(\bar k|k)\) is called the absolute Galois group of k. As a rule, this extension will have infinite degree. It does, however, have the advantage of collecting all finite Galois extensions of k. This is why it is reasonable to
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Every field k is equipped with a distinguished Galois extension: the separable closure \(\bar k|k\). Its Galois group \({G_k} = G(\bar k|k)\) is called the absolute Galois group of k. As a rule, this extension will have infinite degree. It does, however, have the advantage of collecting all finite Galois extensions of k. This is why it is reasonable to
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Integrative oncology: Addressing the global challenges of cancer prevention and treatment
Ca-A Cancer Journal for Clinicians, 2022Jun J Mao,, Msce +2 more
exaly
Radiotheranostics in oncology: Making precision medicine possible
Ca-A Cancer Journal for Clinicians, 2023Eric Aboagye
exaly
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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