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Choice Reviews Online, 2009 This classic book, originally published in 1968, is based on notes of a year-long seminar the authors ran at Princeton University. The primary goal of the book was to give a rather complete presentation of algebraic aspects of global class field theory ...
Artin, Emil, Tate, John
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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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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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