|
This article is cited in 9 scientific papers (total in 9 papers)
Some remarks on the $l$-adic regulator. II
L. V. Kuz'min
Abstract:
Given an algebraic number field $k$ with unit group $U(k)$ and a prime number $l$, consider the bilinear form $S\colon(U(k)\otimes\mathbf Z_l)(U(k)\otimes\mathbf Z_l)\to\mathbf Q_l$, $S(x,y)=\operatorname{Sp}_{k/\mathbf Q}(\log x\cdot\log y)$ where $\log$ is the $l$-adic logarithm. For certain types of fields it is shown that the form $S$ is nondegenerate. We investigate the behavior of the rank of the kernel of $S$ on the family of intermediate fields in
a $\mathbf Z_l$-extension $k_\infty/k$.
Bibliography: 11 titles.
Received: 17.11.1987
Citation:
L. V. Kuz'min, “Some remarks on the $l$-adic regulator. II”, Izv. Akad. Nauk SSSR Ser. Mat., 53:4 (1989), 782–813; Math. USSR-Izv., 35:1 (1990), 113–144
Linking options:
https://www.mathnet.ru/eng/im1274https://doi.org/10.1070/IM1990v035n01ABEH000692 https://www.mathnet.ru/eng/im/v53/i4/p782
|
Statistics & downloads: |
Abstract page: | 267 | Russian version PDF: | 92 | English version PDF: | 10 | References: | 41 | First page: | 1 |
|