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Izv. Akad. Nauk SSSR Ser. Mat., 1989, Volume 53, Issue 4, Pages 782–813 (Mi izv1274)  

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.

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English version:
Mathematics of the USSR-Izvestiya, 1990, 35:1, 113–144

Bibliographic databases:

UDC: 519.4
MSC: Primary 11R23, 11R27; Secondary 11R34, 11S31, 11R33
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

Citation in format AMSBIB
\Bibitem{Kuz89}
\by L.~V.~Kuz'min
\paper Some remarks on the $l$-adic regulator.~II
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1989
\vol 53
\issue 4
\pages 782--813
\mathnet{http://mi.mathnet.ru/izv1274}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1018748}
\zmath{https://zbmath.org/?q=an:0695.12003}
\transl
\jour Math. USSR-Izv.
\yr 1990
\vol 35
\issue 1
\pages 113--144
\crossref{https://doi.org/10.1070/IM1990v035n01ABEH000692}


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    This publication is cited in the following articles:
    1. L. V. Kuz'min, “New explicit formulas for the norm residue symbol, and their applications”, Math. USSR-Izv., 37:3 (1991), 555–586  mathnet  crossref  mathscinet  zmath  adsnasa
    2. L. V. Kuz'min, “An analog of the Riemann–Hurwitz formula for one type of $l$-extensions of algebraic number fields”, Math. USSR-Izv., 36:2 (1991), 325–347  mathnet  crossref  mathscinet  zmath  adsnasa
    3. L. V. Kuz'min, “Some remarks on the $\ell$-adic regulator. III”, Izv. Math., 63:6 (1999), 1089–1138  mathnet  crossref  crossref  mathscinet  zmath  isi
    4. L. V. Kuz'min, “Some remarks on the $\ell$-adic regulator. IV”, Izv. Math., 64:2 (2000), 265–310  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    5. L. V. Kuz'min, “A property of the $\ell$-adic logarithms of units of non-abelian local fields”, Izv. Math., 70:5 (2006), 949–974  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    6. L. V. Kuz'min, “Some remarks on the $\ell$-adic regulator. V. Growth of the $\ell$-adic regulator in the cyclotomic $Z_\ell$-extension of an algebraic number field”, Izv. Math., 73:5 (2009), 959–1021  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    7. L. V. Kuz'min, “The feeble conjecture on the 2-adic regulator for some 2-extensions”, Izv. Math., 76:2 (2012), 346–355  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    8. L. V. Kuz'min, “On a new type of $\ell$-adic regulator for algebraic number fields (the $\ell$-adic regulator without logarithms)”, Izv. Math., 79:1 (2015), 109–144  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    9. L. V. Kuz'min, “Arithmetic of Certain $\ell $-Extensions Ramified at Three Places”, Proc. Steklov Inst. Math., 307 (2019), 65–84  mathnet  crossref  crossref  isi  elib
  • Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
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