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Izv. RAN. Ser. Mat., 2011, Volume 75, Issue 5, Pages 177–194 (Mi izv4279)  

This article is cited in 20 scientific papers (total in 20 papers)

On the standard conjecture of Lefschetz type for complex projective threefolds. II

S. G. Tankeev

Vladimir State University

Abstract: We show that Grothendieck's standard conjecture of Lefschetz type on the algebraicity of the operators $\ast$ and $\Lambda$ of Hodge theory holds for all smooth complex projective threefolds of Kodaira dimension $\varkappa<3$.

Keywords: complex projective threefold of non-basic type, standard conjecture of Lefschetz type, Friedlander–Mazur conjecture.

DOI: https://doi.org/10.4213/im4279

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English version:
Izvestiya: Mathematics, 2011, 75:5, 1047–1062

Bibliographic databases:

UDC: 512.6
MSC: 14C25, 14F25, 14J30
Received: 28.12.2009
Revised: 20.04.2010

Citation: S. G. Tankeev, “On the standard conjecture of Lefschetz type for complex projective threefolds. II”, Izv. RAN. Ser. Mat., 75:5 (2011), 177–194; Izv. Math., 75:5 (2011), 1047–1062

Citation in format AMSBIB
\by S.~G.~Tankeev
\paper On the standard conjecture of Lefschetz type for complex projective threefolds.~II
\jour Izv. RAN. Ser. Mat.
\yr 2011
\vol 75
\issue 5
\pages 177--194
\jour Izv. Math.
\yr 2011
\vol 75
\issue 5
\pages 1047--1062

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  • https://doi.org/10.4213/im4279
  • http://mi.mathnet.ru/eng/izv/v75/i5/p177

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    This publication is cited in the following articles:
    1. S. G. Tankeev, “On the standard conjecture for complex 4-dimensional elliptic varieties”, Izv. Math., 76:5 (2012), 967–990  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    2. O. V. Nikol'skaya, “On algebraic cycles on a fibre product of families of K3-surfaces”, Izv. Math., 77:1 (2013), 143–162  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    3. S. G. Tankeev, “On the standard conjecture for complex 4-dimensional elliptic varieties and compactifications of Néron minimal models”, Izv. Math., 78:1 (2014), 169–200  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    4. S. G. Tankeev, “On the standard conjecture and the existence of a Chow–Lefschetz decomposition for complex projective varieties”, Izv. Math., 79:1 (2015), 177–207  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    5. R. Laterveer, “Yet another version of Mumford's theorem”, Arch. Math. (Basel), 104:2 (2015), 125–131  crossref  mathscinet  zmath  isi  scopus
    6. O. V. Nikolskaya, “Ob algebraicheskikh tsiklakh na rassloennykh proizvedeniyakh neizotrivialnykh semeistv regulyarnykh poverkhnostei s geometricheskim rodom 1”, Model. i analiz inform. sistem, 23:4 (2016), 440–465  mathnet  crossref  mathscinet  elib
    7. Laterveer R., “Some desultory remarks concerning algebraic cycles and Calabi–Yau threefolds”, Rend. Circ. Mat. Palermo, 65:2 (2016), 333–344  crossref  mathscinet  zmath  isi  elib  scopus
    8. Laterveer R., “On a multiplicative version of Mumford's theorem”, Abh. Math. Semin. Univ. Hamburg, 86:1 (2016), 89–96  crossref  mathscinet  zmath  isi  scopus
    9. S. G. Tankeev, “On an inductive approach to the standard conjecture for a fibred complex variety with strong semistable degeneracies”, Izv. Math., 81:6 (2017), 1253–1285  mathnet  crossref  crossref  adsnasa  isi  elib
    10. Suh Junecue, “Standard conjecture of Künneth type with torsion coefficients”, Algebra Number Theory, 11:7 (2017), 1573–1596  crossref  mathscinet  zmath  isi  scopus
    11. Laterveer R., “Some New Examples of Smash-Nilpotent Algebraic Cycles”, Glasg. Math. J., 59:3, 3 (2017), 623–634  crossref  mathscinet  zmath  isi  scopus
    12. Lehmann B., Ottem J.Ch., “Positivity of the Diagonal”, Adv. Math., 335 (2018), 664–695  crossref  mathscinet  zmath  isi  scopus
    13. S. G. Tankeev, “On the Standard Conjecture for a 3-Dimensional Variety Fibered over a Surface”, Math. Notes, 105:4 (2019), 636–637  mathnet  crossref  crossref  mathscinet  isi  elib
    14. S. G. Tankeev, “On the standard conjecture for a fibre product of three elliptic surfaces with pairwise-disjoint discriminant loci”, Izv. Math., 83:3 (2019), 613–653  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    15. Laterveer R., Nagel J., Peters Ch., “On Complete Intersections in Varieties With Finite-Dimensional Motive”, Q. J. Math., 70:1 (2019), 71–104  crossref  mathscinet  zmath  isi  scopus
    16. S. G. Tankeev, “On algebraic isomorphisms of rational cohomology of a Künneman compactification of the Néron minimal model”, Sib. elektron. matem. izv., 17 (2020), 89–125  mathnet  crossref
    17. Bini G., Laterveer R., Pacienza G., “Voisin'S Conjecture For Zero-Cycles on Calabi-Yau Varieties and Their Mirrors”, Adv. Geom., 20:1 (2020), 91–108  crossref  isi
    18. S. G. Tankeev, “On the standard conjecture for a $3$-dimensional variety fibred by curves with a non-injective Kodaira–Spencer map”, Izv. Math., 84:5 (2020), 1016–1035  mathnet  crossref  crossref  mathscinet  isi  elib
    19. S. G. Tankeev, “On the standard conjecture for projective compactifications of Néron models of $3$-dimensional Abelian varieties”, Izv. Math., 85:1 (2021), 145–175  mathnet  crossref  crossref  mathscinet  isi  elib
    20. S. G. Tankeev, “On the Standard Conjecture for Compactifications of Néron Models of Three-Dimensional Abelian Varieties with Multiplications in an Imaginary Quadratic Field”, Math. Notes, 109:3 (2021), 498–499  mathnet  crossref  crossref  mathscinet  isi  elib
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