Geodesic
On a~new type of $\ell$-adic regulator for algebraic number fields (the $\ell$-adic regulator without logarithms)
Izvestiya. Mathematics , Tome 79 (2015) no. 1, pp. 109-144

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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. 
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     author = {L. V. Kuz'min},
     title = {On a~new type of $\ell$-adic regulator for algebraic number fields (the $\ell$-adic regulator without logarithms)},
     journal = {Izvestiya. Mathematics },
     pages = {109--144},
     publisher = {mathdoc},
     volume = {79},
     number = {1},
     year = {2015},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_2015_79_1_a5/}
}
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L. V. Kuz'min. On a~new type of $\ell$-adic regulator for algebraic number fields (the $\ell$-adic regulator without logarithms). Izvestiya. Mathematics , Tome 79 (2015) no. 1, pp. 109-144. http://geodesic.mathdoc.fr/item/IM2_2015_79_1_a5/