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This article is cited in 20 scientific papers (total in 20 papers)
Explicit construction of class field theory for a multidimensional local field
S. V. Vostokov
Abstract:
Let $k$ be a finite extension of the field of $p$-adic numbers $\mathbf Q_p$ and $k\{\{t\}\}$ the field of Laurent series $\sum_{-\infty}^\infty a_it^i$ for which the $a_i$ are bounded in the norm of $k$ and $a_i\to0$ as $i\to-\infty$. In the $n$-dimensional local field $F=k\{\{t_1\}\}\cdots\{\{t_{n-1}\}\}$ a pairing is given in explicit form between the completed Milnor $k$-functor $K_n^{\mathrm{top}}(F)$ and the multiplicative group $F^*$ with values in the group of $q=p^m$th roots of unity.
Bibliography: 14 titles.
Received: 01.12.1983
Citation:
S. V. Vostokov, “Explicit construction of class field theory for a multidimensional local field”, Izv. Akad. Nauk SSSR Ser. Mat., 49:2 (1985), 283–308; Math. USSR-Izv., 26:2 (1986), 263–287
Linking options:
https://www.mathnet.ru/eng/im1355https://doi.org/10.1070/IM1986v026n02ABEH001141 https://www.mathnet.ru/eng/im/v49/i2/p283
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Abstract page: | 464 | Russian version PDF: | 179 | English version PDF: | 15 | References: | 53 | First page: | 1 |
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