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Izv. Akad. Nauk SSSR Ser. Mat., 1972, Volume 36, Issue 2, Pages 267–327 (Mi izv2298)  

This article is cited in 22 scientific papers (total in 22 papers)

The Tate module for algebraic number fields

L. V. Kuz'min


Abstract: In this article we examine some hypotheses concerning the structure of the Tate module of an algebraic number field. We also examine the connection between these hypotheses and some problems in the theory of extensions with specific branch points. The proofs of these hypotheses are given for several special cases.
Our definition of the Tate module differs somewhat from the one generally accepted.

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English version:
Mathematics of the USSR-Izvestiya, 1972, 6:2, 263–321

Bibliographic databases:

UDC: 519.4
MSC: Primary 13C10; Secondary 12A35, 12A65, 12B10
Received: 07.10.1971

Citation: L. V. Kuz'min, “The Tate module for algebraic number fields”, Izv. Akad. Nauk SSSR Ser. Mat., 36:2 (1972), 267–327; Math. USSR-Izv., 6:2 (1972), 263–321

Citation in format AMSBIB
\Bibitem{Kuz72}
\by L.~V.~Kuz'min
\paper The Tate module for algebraic number fields
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1972
\vol 36
\issue 2
\pages 267--327
\mathnet{http://mi.mathnet.ru/izv2298}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=304353}
\zmath{https://zbmath.org/?q=an:0231.12013}
\transl
\jour Math. USSR-Izv.
\yr 1972
\vol 6
\issue 2
\pages 263--321
\crossref{https://doi.org/10.1070/IM1972v006n02ABEH001875}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. L. V. Kuz'min, “Cohomological dimension of some Galois groups”, Math. USSR-Izv., 9:3 (1975), 455–463  mathnet  crossref  mathscinet  zmath
    2. L. V. Kuz'min, “Local extensions associated with $l$-extensions with given ramification”, Math. USSR-Izv., 9:4 (1975), 693–726  mathnet  crossref  mathscinet  zmath
    3. V. A. Babaitsev, “On some questions in the theory of $\Gamma$-extensions of algebraic number fields”, Math. USSR-Izv., 10:3 (1976), 453–462  mathnet  crossref  mathscinet  zmath
    4. V. A. Babaitsev, “On some questions in the theory of $\Gamma$-extensions of algebraic number fields. II”, Math. USSR-Izv., 10:4 (1976), 675–685  mathnet  crossref  mathscinet  zmath
    5. L. V. Kuz'min, “Some duality theorems for cyclotomic $\Gamma$-extensions of algebraic number fields of $CM$ type”, Math. USSR-Izv., 14:3 (1980), 441–498  mathnet  crossref  mathscinet  zmath  isi
    6. V. A. Babaitsev, “On the boundedness of the Iwasawa invariant”, Math. USSR-Izv., 16:1 (1981), 1–19  mathnet  crossref  mathscinet  zmath  isi
    7. L. V. Kuz'min, “Some remarks on the $l$-adic Dirichlet theorem and the $l$-adic regulator”, Math. USSR-Izv., 19:3 (1982), 445–478  mathnet  crossref  mathscinet  zmath
    8. L. V. Kuz'min, “Some remarks on the $l$-adic regulator. II”, Math. USSR-Izv., 35:1 (1990), 113–144  mathnet  crossref  mathscinet  zmath
    9. L. V. Kuz'min, “New explicit formulas for the norm residue symbol, and their applications”, Math. USSR-Izv., 37:3 (1991), 555–586  mathnet  crossref  mathscinet  zmath  adsnasa
    10. L. V. Kuz'min, “An analog of the Riemann–Hurwitz formula for one type of $l$-extensions of algebraic number fields”, Math. USSR-Izv., 36:2 (1991), 325–347  mathnet  crossref  mathscinet  zmath  adsnasa
    11. L. V. Kuz'min, “On formulae for the class number of real Abelian fields”, Izv. Math., 60:4 (1996), 695–761  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    12. Belliard J.R., Do T.N.Q., “Class formulae for real abelian fields”, Annales de l Institut Fourier, 51:4 (2001), 903–937  isi
    13. David Vauclair, “Cup-produit, Noyaux de Capitulation étales et Conjecture de Greenberg Généralisée”, K-Theory, 36:3-4 (2005), 223  crossref  mathscinet  zmath  isi
    14. I. S. Rakhimov, “O povedenii arifmeticheskikh invariantov nekotorogo klassa ellipticheskikh krivykh v krugovykh $\Gamma$-rasshireniyakh”, Matem. tr., 8:1 (2005), 122–134  mathnet  mathscinet  zmath  elib
    15. Belliard J.R., Nguyen-Quang-Do T., “On modified circular units and annihilation of real classes”, Nagoya Mathematical Journal, 177 (2005), 77–115  isi
    16. NGUYEN QUANG DO THONG, “SUR LA CONJECTURE FAIBLE DE GREENBERG DANS LE CAS ABÉLIEN p-DÉCOMPOSÉ”, Int. J. Number Theory, 02:01 (2006), 49  crossref
    17. Seo, S, “On formulas for the index of the circular distributions”, Manuscripta Mathematica, 127:3 (2008), 381  crossref  isi  elib
    18. L. V. Kuz'min, “Some remarks on the $\ell$-adic regulator. V. Growth of the $\ell$-adic regulator in the cyclotomic $Z_\ell$-extension of an algebraic number field”, Izv. Math., 73:5 (2009), 959–1021  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    19. Belliard J.-Robert, “Asymptotic Cohomology of Circular Units”, International Journal of Number Theory, 5:7 (2009), 1205–1219  crossref  isi
    20. A. Movahhedi, T. Nguyen Quang Do, “On universal norms and the first layers of
      $$\mathbb {Z}_p$$
      Z p -extensions of a number field”, Math. Ann, 2014  crossref
    21. L. V. Kuz'min, “On a new type of $\ell$-adic regulator for algebraic number fields (the $\ell$-adic regulator without logarithms)”, Izv. Math., 79:1 (2015), 109–144  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    22. 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  mathnet  crossref  crossref  adsnasa  isi  elib
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