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Izvestiya: Mathematics, 2015, Volume 79, Issue 1, Pages 109–144
DOI: https://doi.org/10.1070/IM2015v079n01ABEH002736
(Mi im8177)
 

This article is cited in 2 scientific papers (total in 2 papers)

On a new type of $\ell$-adic regulator for algebraic number fields (the $\ell$-adic regulator without logarithms)

L. V. Kuz'min

National Research Centre "Kurchatov Institute"
References:
Abstract: For an algebraic number field $K$ such that a prime $\ell$ splits completely in $K$, we define a regulator $\mathfrak R_\ell(K)\in\mathbb Z_\ell$ that characterizes the subgroup of universal norms from the cyclotomic $\mathbb Z_\ell$-extension of $K$ in the completed group of $S$-units of $K$, where $S$ consists of all prime divisors of $\ell$. We prove that the inequality $\mathfrak R_\ell(K)\ne0$ follows from the $\ell$-adic Schanuel conjecture and holds for some Abelian extensions of imaginary quadratic fields. We study the connection between the regulator $\mathfrak R_\ell(K)$ and the feeble conjecture on the $\ell$-adic regulator, and define analogues of the Gross regulator.
Keywords: $\ell$-adic regulator, $S$-units, global universal norm, Schanuel conjecture, Iwasawa theory.
Funding agency Grant number
Russian Foundation for Basic Research 11-01-00588-a
This paper was written with the financial support of the Russian Foundation for Basic Research (grant no. 11-01-00588-a).
Received: 16.10.2013
Russian version:
Izvestiya Rossiiskoi Akademii Nauk. Seriya Matematicheskaya, 2015, Volume 79, Issue 1, Pages 115–152
DOI: https://doi.org/10.4213/im8177
Bibliographic databases:
Document Type: Article
UDC: 511.236.3
MSC: 11R23, 11R18
Language: English
Original paper language: Russian
Citation: L. V. Kuz'min, “On a new type of $\ell$-adic regulator for algebraic number fields (the $\ell$-adic regulator without logarithms)”, Izv. RAN. Ser. Mat., 79:1 (2015), 115–152; Izv. Math., 79:1 (2015), 109–144
Citation in format AMSBIB
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\paper On a~new type of $\ell$-adic regulator for algebraic number fields (the $\ell$-adic regulator without logarithms)
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\pages 115--152
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\vol 79
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  • https://doi.org/10.1070/IM2015v079n01ABEH002736
  • https://www.mathnet.ru/eng/im/v79/i1/p115
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    Citing articles in Google Scholar: Russian citations, English citations
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    Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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    Abstract page:423
    Russian version PDF:174
    English version PDF:18
    References:38
    First page:6
     
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