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., 1979, Volume 43, Issue 2, Pages 418–429 (Mi izv1719)  

This article is cited in 5 scientific papers (total in 5 papers)

On algebraic cycles on Abelian varieties. II

S. G. Tankeev


Abstract: Let $I$ be a simple 4-dimensional Abelian variety of the first or second type in Albert's classification (i.e. all simple factors of the $\mathbf R$-algebra $[\operatorname{End}I]\otimes_\mathbf Z\mathbf R$ are isomorphic to $\mathbf R$ or $M_2(\mathbf R)$). In this case the algebra $\bigoplus H^{2p}(I,\mathbf Q)\cap H^{p,p}$ over $\mathbf Q$ is generated by divisor classes. If $\dim I=5$, $\operatorname{End}(I)\overset\sim\longrightarrow\mathbf Z$ and the Hodge group $\mathrm{Hg}(I)$ has type $A_1$ or $A_1\times A_1$, then $\dim_\mathbf QH^4(I,\mathbf Q)\cap H^{2,2}=2$ and the $\mathbf Q$-space $H^4(I,\mathbf Q)\cap H^{2,2}$ is not generated by classes of intersections of divisors.
Bibliography: 6 titles.

Full text: PDF file (837 kB)
References: PDF file   HTML file

English version:
Mathematics of the USSR-Izvestiya, 1980, 14:2, 383–394

Bibliographic databases:

UDC: 513.6
MSC: Primary 14C30, 14K20; Secondary 20G05
Received: 12.09.1978

Citation: S. G. Tankeev, “On algebraic cycles on Abelian varieties. II”, Izv. Akad. Nauk SSSR Ser. Mat., 43:2 (1979), 418–429; Math. USSR-Izv., 14:2 (1980), 383–394

Citation in format AMSBIB
\Bibitem{Tan79}
\by S.~G.~Tankeev
\paper On~algebraic cycles on Abelian varieties.~II
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1979
\vol 43
\issue 2
\pages 418--429
\mathnet{http://mi.mathnet.ru/izv1719}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=534601}
\zmath{https://zbmath.org/?q=an:0429.14014|0409.14008}
\transl
\jour Math. USSR-Izv.
\yr 1980
\vol 14
\issue 2
\pages 383--394
\crossref{https://doi.org/10.1070/IM1980v014n02ABEH001117}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1980KM96800010}


Linking options:
  • http://mi.mathnet.ru/eng/izv1719
  • http://mi.mathnet.ru/eng/izv/v43/i2/p418

    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
    Cycle of papers

    This publication is cited in the following articles:
    1. S. G. Tankeev, “On algebraic cycles on surfaces and Abelian varieties”, Math. USSR-Izv., 18:2 (1982), 349–380  mathnet  crossref  mathscinet  zmath
    2. 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
    3. S. G. Tankeev, “Cycles on Abelian varieties and exceptional numbers”, Izv. Math., 60:2 (1996), 391–424  mathnet  crossref  crossref  mathscinet  zmath  isi
    4. Izv. Math., 60:2 (1996), 379–389  mathnet  crossref  crossref  mathscinet  zmath  isi
    5. Orr M., “Lower Bounds For Ranks of Mumford-Tate Groups”, Bull. Soc. Math. Fr., 143:2 (2015), 229–246  isi
  • Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
    Number of views:
    This page:261
    Full text:65
    References:44
    First page:1

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