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Izv. RAN. Ser. Mat., 2000, Volume 64, Issue 2, Pages 43–88 (Mi izv284)  

This article is cited in 4 scientific papers (total in 4 papers)

Some remarks on the $\ell$-adic regulator. IV

L. V. Kuz'min

Russian Research Centre "Kurchatov Institute"

Abstract: We continue to examine the bilinear form $U(K_n)\times U(K_n)\to\mathbb{Q}_\ell$, $(x,y)\to\operatorname{Sp}_{K_n/\mathbb{Q}_\ell}(\log x\cdot\log y)$ where $K_n$ runs through all intermediate subfields of the cyclotomic $\mathbb{Z}_\ell$-extension $K_\infty/K$, $K$ is an arbitrary finite extension of $\mathbb{Q}_\ell$, and $\log$ is the $\ell$-adic logarithm. We give applications to the weak conjecture on the $\ell$-adic regulator. In particular, we prove this conjecture for $\ell$-extensions of Abelian number fields.

DOI: https://doi.org/10.4213/im284

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English version:
Izvestiya: Mathematics, 2000, 64:2, 265–310

Bibliographic databases:

MSC: 11S85, 11S25
Received: 23.02.1999

Citation: L. V. Kuz'min, “Some remarks on the $\ell$-adic regulator. IV”, Izv. RAN. Ser. Mat., 64:2 (2000), 43–88; Izv. Math., 64:2 (2000), 265–310

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    This publication is cited in the following articles:
    1. 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
    2. 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
    3. 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
    4. 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
  • Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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