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Titlebook: Cyclotomic Fields I and II; Serge Lang Textbook 1990Latest edition Springer Science+Business Media New York 1990 Cohomology.Prime.algebra.

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书目名称Cyclotomic Fields I and II
编辑Serge Lang
视频video
丛书名称Graduate Texts in Mathematics
图书封面Titlebook: Cyclotomic Fields I and II;  Serge Lang Textbook 1990Latest edition Springer Science+Business Media New York 1990 Cohomology.Prime.algebra.
描述Kummer‘s work on cyclotomic fields paved the way for the development of algebraic number theory in general by Dedekind, Weber, Hensel, Hilbert, Takagi, Artin and others. However, the success of this general theory has tended to obscure special facts proved by Kummer about cyclotomic fields which lie deeper than the general theory. For a long period in the 20th century this aspect of Kummer‘s work seems to have been largely forgotten, except for a few papers, among which are those by Pollaczek [Po], Artin-Hasse [A-H] and Vandiver [Va]. In the mid 1950‘s, the theory of cyclotomic fields was taken up again by Iwasawa and Leopoldt. Iwasawa viewed cyclotomic fields as being analogues for number fields of the constant field extensions of algebraic geometry, and wrote a great sequence of papers investigating towers of cyclotomic fields, and more generally, Galois extensions of number fields whose Galois group is isomorphic to the additive group of p-adic integers. Leopoldt concentrated on a fixed cyclotomic field, and established various p-adic analogues of the classical complex analytic class number formulas. In particular, this led him to introduce, with Kubota, p-adic analogues of the
出版日期Textbook 1990Latest edition
关键词Cohomology; Prime; algebra; finite field; homomorphism; number theory
版次2
doihttps://doi.org/10.1007/978-1-4612-0987-4
isbn_softcover978-1-4612-6972-4
isbn_ebook978-1-4612-0987-4Series ISSN 0072-5285 Series E-ISSN 2197-5612
issn_series 0072-5285
copyrightSpringer Science+Business Media New York 1990
The information of publication is updating

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The ,-adic ,-function,rive further analytic properties, which allow us to make explicit its value at . = 1, thereby obtaining Leopoldt’s formula in the .-adic case, analogous to that of the complex case. We also give Leopoldt’s version of the .-adic class number formula and regulator.
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0072-5285 rt, Takagi, Artin and others. However, the success of this general theory has tended to obscure special facts proved by Kummer about cyclotomic fields which lie deeper than the general theory. For a long period in the 20th century this aspect of Kummer‘s work seems to have been largely forgotten, ex
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The Elephant’s I: Looking for Abu’l Abbas can be used to construct explicitly such eigenspaces. The first section lays the foundations for the special type of ring under consideration. After that we study the Artin-Schreier equation and the Frobenius endomorphism.
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