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Izv. Akad. Nauk SSSR Ser. Mat., 1981, Volume 45, Issue 2, Pages 398–434 (Mi izv1560)  

This article is cited in 16 scientific papers (total in 16 papers)

On algebraic cycles on surfaces and Abelian varieties

S. G. Tankeev


Abstract: This paper contains a proof of the Tate conjecture on algebraic cycles on surfaces with strongly degenerate reduction over function fields and the Hodge conjecture on cycles on simple Abelian varieties of the first and second types according to Albert's classification (under certain restrictions on the dimension of the variety and the center of its ring of endomorphisms).
Bibliography: 27 titles.

Full text: PDF file (3179 kB)
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English version:
Mathematics of the USSR-Izvestiya, 1982, 18:2, 349–380

Bibliographic databases:

UDC: 513.6
MSC: Primary 14G13, 14C30, 32J25, 14F30; Secondary 14J05, 14E25, 14K22, 14K05, 14K20
Received: 21.11.1980

Citation: S. G. Tankeev, “On algebraic cycles on surfaces and Abelian varieties”, Izv. Akad. Nauk SSSR Ser. Mat., 45:2 (1981), 398–434; Math. USSR-Izv., 18:2 (1982), 349–380

Citation in format AMSBIB
\Bibitem{Tan81}
\by S.~G.~Tankeev
\paper On~algebraic cycles on surfaces and Abelian varieties
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1981
\vol 45
\issue 2
\pages 398--434
\mathnet{http://mi.mathnet.ru/izv1560}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=616226}
\zmath{https://zbmath.org/?q=an:0551.14010|0493.14014}
\transl
\jour Math. USSR-Izv.
\yr 1982
\vol 18
\issue 2
\pages 349--380
\crossref{https://doi.org/10.1070/IM1982v018n02ABEH001390}


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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. S. G. Tankeev, “On algebraic cycles on simple 5-dimensional Abelian varieties”, Math. USSR-Izv., 19:1 (1982), 95–123  mathnet  crossref  mathscinet  zmath
    2. S. G. Tankeev, “On cycles on Abelian varieties of prime dimension over finite or number fields”, Math. USSR-Izv., 22:2 (1984), 329–337  mathnet  crossref  mathscinet  zmath
    3. G. A. Mustafin, “Families of algebraic varieties and invariant cycles”, Math. USSR-Izv., 27:2 (1986), 251–278  mathnet  crossref  mathscinet  zmath
    4. S. G. Tankeev, “Cycles on simple Abelian varieties of prime dimension over number fields”, Math. USSR-Izv., 31:3 (1988), 527–540  mathnet  crossref  mathscinet  zmath
    5. S. G. Tankeev, “K3 surfaces over number fields and $l$-adic representations”, Math. USSR-Izv., 33:3 (1989), 575–595  mathnet  crossref  mathscinet  zmath
    6. 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
    7. S. G. Tankeev, “Abelian varieties and the general Hodge conjecture”, Russian Acad. Sci. Izv. Math., 43:1 (1994), 179–191  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    8. 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
    9. 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
    10. S. G. Tankeev, “Cycles on Abelian varieties and exceptional numbers”, Izv. Math., 60:2 (1996), 391–424  mathnet  crossref  crossref  mathscinet  zmath  isi
    11. S. G. Tankeev, “Cycles of small codimension on a simple $2p$- or $4p$-dimensional Abelian variety”, Izv. Math., 63:6 (1999), 1221–1262  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    12. S. G. Tankeev, “On the Brauer group”, Izv. Math., 64:4 (2000), 787–806  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    13. S. G. Tankeev, “On the Brauer group of an arithmetic scheme”, Izv. Math., 65:2 (2001), 357–388  mathnet  crossref  crossref  mathscinet  zmath  elib
    14. S. G. Tankeev, “On the standard conjecture for complex Abelian schemes over smooth projective curves”, Izv. Math., 67:3 (2003), 597–635  mathnet  crossref  crossref  mathscinet  zmath  isi
    15. S. G. Tankeev, “On the Brauer group of an arithmetic scheme. II”, Izv. Math., 67:5 (2003), 1007–1029  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    16. S. G. Tankeev, “On algebraic cycles on complex Abelian schemes over smooth projective curves”, Izv. Math., 72:4 (2008), 817–844  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
  • Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
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