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Springer Monographs in Mathematics, 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 ...
Georges Gras
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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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Senior Honors Thesis, Department of Mathematics, University of Wisconsin-MadisonIn this thesis, we discuss the main theorems and proofs of local and global class field theory, which give a complete description for the abelian extensions of local fields ...
Mouli, Haran
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Grundlehren Der Mathematischen Wissenschaften in Einzeldarstellungen Mit Besonderer Berücksichtigung Der Anwendungsgebiete, 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)).
Jürgen Neukirch
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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)).
Jürgen Neukirch
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The Annals of Mathematics, 1950
Local class field theory is treated by means of cohomology theory. Let \(L/K\) be a Galois extension with Galois group \(\mathfrak L\). Let \(\mathfrak H\) be an invariant subgroup of \(\mathfrak L\), and \(F\) be the corresponding subfield of \(L\). The lifting \(\lambda\) of the Galois 2-cohomology group \(H^2(\mathfrak L/\mathfrak H, F^*)\) \((F^*\)
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Local class field theory is treated by means of cohomology theory. Let \(L/K\) be a Galois extension with Galois group \(\mathfrak L\). Let \(\mathfrak H\) be an invariant subgroup of \(\mathfrak L\), and \(F\) be the corresponding subfield of \(L\). The lifting \(\lambda\) of the Galois 2-cohomology group \(H^2(\mathfrak L/\mathfrak H, F^*)\) \((F^*\)
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A Generalization of Global Class Field Theory
Canadian Journal of Mathematics, 1969Let R be a field of rational functions of one variable over a field of constants R0. Dock Sang Rim (6) has proved that the global reciprocity law in exactly the usual sense holds whenever R0 is an absolutely algebraic quasi-fini te field of characteristic not equal to 0: this was known before only when R0 was a finite field. We shall give another proof
Seo, Tae Kun, Whaples, G.
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1988
Let k be a finite field with q = pn elements and let V be an algebraic variety defined over k (or, as one also says, a k-variety). Suppose that V is defined by charts Ui (isomorphic to affine k-varieties) and changes of coordinates uij (with coefficients in k).
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Let k be a finite field with q = pn elements and let V be an algebraic variety defined over k (or, as one also says, a k-variety). Suppose that V is defined by charts Ui (isomorphic to affine k-varieties) and changes of coordinates uij (with coefficients in k).
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