RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
 General information Latest issue Forthcoming papers Archive Impact factor Subscription Guidelines for authors License agreement Submit a manuscript Search papers Search references RSS Latest issue Current issues Archive issues What is RSS

 Izv. RAN. Ser. Mat.: Year: Volume: Issue: Page: Find

 Izv. RAN. Ser. Mat., 2015, Volume 79, Issue 1, Pages 115–152 (Mi izv8177)

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: PDF file (751 kB)
References: PDF file   HTML file

English version:
Izvestiya: Mathematics, 2015, 79:1, 109–144

Bibliographic databases:

UDC: 511.236.3
MSC: 11R23, 11R18

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
\Bibitem{Kuz15} \by L.~V.~Kuz'min \paper On a~new type of $\ell$-adic regulator for algebraic number fields (the $\ell$-adic regulator without logarithms) \jour Izv. RAN. Ser. Mat. \yr 2015 \vol 79 \issue 1 \pages 115--152 \mathnet{http://mi.mathnet.ru/izv8177} \crossref{https://doi.org/10.4213/im8177} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=3352584} \zmath{https://zbmath.org/?q=an:06428107} \adsnasa{http://adsabs.harvard.edu/cgi-bin/bib_query?2015IzMat..79..109K} \elib{https://elibrary.ru/item.asp?id=23421416} \transl \jour Izv. Math. \yr 2015 \vol 79 \issue 1 \pages 109--144 \crossref{https://doi.org/10.1070/IM2015v079n01ABEH002736} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000350754500006} \scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84924333058} 

• http://mi.mathnet.ru/eng/izv8177
• https://doi.org/10.4213/im8177
• http://mi.mathnet.ru/eng/izv/v79/i1/p115

 SHARE:

Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles
Cycle of papers

This publication is cited in the following articles:
1. 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
2. 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
•  Number of views: This page: 277 Full text: 83 References: 19 First page: 6