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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.
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
Linking options:
https://www.mathnet.ru/eng/im8177https://doi.org/10.1070/IM2015v079n01ABEH002736 https://www.mathnet.ru/eng/im/v79/i1/p115
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Abstract page: | 423 | Russian version PDF: | 174 | English version PDF: | 18 | References: | 38 | First page: | 6 |
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