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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"
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). |
DOI:
https://doi.org/10.4213/im8177
 Full text:
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English version:
Izvestiya: Mathematics, 2015, 79:1, 109–144
Bibliographic databases:
     
UDC:
511.236.3
MSC: 11R23, 11R18
Received: 16.10.2013
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
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Cycle of papers
This publication is cited in the following articles:
-
L. V. Kuz'min, “On a new type of $\ell$-adic regulator for algebraic number fields. II”, St. Petersburg Math. J., 27:6 (2016), 977–984
 -
L. V. Kuz'min, “Local and global universal norms in the cyclotomic $\mathbb Z_\ell$-extension
of an algebraic number field”, Izv. Math., 82:3 (2018), 532–548
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