Izvestiya Akademii Nauk SSSR. Seriya Matematicheskaya
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






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


Izv. Akad. Nauk SSSR Ser. Mat., 1987, Volume 51, Issue 6, Pages 1214–1227 (Mi izv1338)  

This article is cited in 8 scientific papers (total in 8 papers)

Cycles on simple Abelian varieties of prime dimension over number fields

S. G. Tankeev


Abstract: For all simple Abelian varieties of prime dimension over number fields the author proves 1) a version of the Mumford–Tate conjecture, asserting that the Lie algebra of the image of the $l$-adic representation is isomorphic to the Lie algebra of the set of $\mathbf Q_l$-points of the Mumford–Tate group, and 2) the Tate conjecture on cycles.
Bibliography: 21 titles.

Full text: PDF file (1485 kB)
References: PDF file   HTML file

English version:
Mathematics of the USSR-Izvestiya, 1988, 31:3, 527–540

Bibliographic databases:

UDC: 513.6
MSC: 14K15, 14C99
Received: 24.12.1985

Citation: S. G. Tankeev, “Cycles on simple Abelian varieties of prime dimension over number fields”, Izv. Akad. Nauk SSSR Ser. Mat., 51:6 (1987), 1214–1227; Math. USSR-Izv., 31:3 (1988), 527–540

Citation in format AMSBIB
\Bibitem{Tan87}
\by S.~G.~Tankeev
\paper Cycles on simple Abelian varieties of prime dimension over number fields
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1987
\vol 51
\issue 6
\pages 1214--1227
\mathnet{http://mi.mathnet.ru/izv1338}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=933962}
\zmath{https://zbmath.org/?q=an:0681.14022|0656.14023}
\transl
\jour Math. USSR-Izv.
\yr 1988
\vol 31
\issue 3
\pages 527--540
\crossref{https://doi.org/10.1070/IM1988v031n03ABEH001088}


Linking options:
  • http://mi.mathnet.ru/eng/izv1338
  • http://mi.mathnet.ru/eng/izv/v51/i6/p1214

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


    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. S. G. Tankeev, “K3 surfaces over number fields and the Mumford–Tate conjecture”, Math. USSR-Izv., 37:1 (1991), 191–208  mathnet  crossref  mathscinet  zmath  adsnasa
    2. S. G. Tankeev, “Kuga–Satake abelian varieties and $l$-adic representations”, Math. USSR-Izv., 39:1 (1992), 855–867  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    3. S. G. Tankeev, “Algebraic cycles on an abelian variety without complex multiplication”, Russian Acad. Sci. Izv. Math., 44:3 (1995), 531–553  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    4. S. G. Tankeev, “Surfaces of type K3 over number fields and the Mumford–Tate conjecture. II”, Izv. Math., 59:3 (1995), 619–646  mathnet  crossref  mathscinet  zmath  isi
    5. S. G. Tankeev, “Cycles on Abelian varieties and exceptional numbers”, Izv. Math., 60:2 (1996), 391–424  mathnet  crossref  crossref  mathscinet  zmath  isi
    6. S. G. Tankeev, “On Frobenius traces”, Izv. Math., 62:1 (1998), 157–190  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    7. S. G. Tankeev, “On weights of the $l$-adic representation and arithmetic of Frobenius eigenvalues”, Izv. Math., 63:1 (1999), 181–218  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    8. O. V. Oreshkina (Nikolskaya), “O gipotezakh Khodzha, Teita i Mamforda–Teita dlya rassloennykh proizvedenii semeistv regulyarnykh poverkhnostei s geometricheskim rodom 1”, Model. i analiz inform. sistem, 25:3 (2018), 312–322  mathnet  crossref  elib
  • Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
    Number of views:
    This page:229
    Full text:88
    References:40
    First page:1

     
    Contact us:
     Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2021