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. RAN. Ser. Mat., 2002, Volume 66, Issue 2, Pages 173–204 (Mi izv383)  

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

The arithmetic and geometry of a generic hypersurface section

S. G. Tankeev

Vladimir State University

Abstract: If the Hodge conjecture (respectively the Tate conjecture or the Mumford–Tate conjecture) holds for a smooth projective variety $X$ over a field $k$ of characteristic zero, then it holds for a generic member $X_t$ of a $k$-rational Lefschetz pencil of hypersurface sections of $X$ of sufficiently high degree. The Mumford–Tate conjecture is true for the Hodge $\mathbb{Q}$-structure associated with vanishing cycles on $X_t$. If the transcendental part of the second cohomology of a K3 surface $S$ over a number field is an absolutely irreducible module under the action of the Hodge group $\operatorname{Hg}(S)$, then the punctual Hilbert scheme $\operatorname{Hilb}^2(S)$ is a hyperkähler fourfold satisfying the conjectures of Hodge, Tate and Mumford–Tate.

DOI: https://doi.org/10.4213/im383

Full text: PDF file (2482 kB)
References: PDF file   HTML file

English version:
Izvestiya: Mathematics, 2002, 66:2, 393–424

Bibliographic databases:

UDC: 512.6
MSC: 14K15
Received: 31.10.2000

Citation: S. G. Tankeev, “The arithmetic and geometry of a generic hypersurface section”, Izv. RAN. Ser. Mat., 66:2 (2002), 173–204; Izv. Math., 66:2 (2002), 393–424

Citation in format AMSBIB
\Bibitem{Tan02}
\by S.~G.~Tankeev
\paper The arithmetic and geometry of a~generic hypersurface section
\jour Izv. RAN. Ser. Mat.
\yr 2002
\vol 66
\issue 2
\pages 173--204
\mathnet{http://mi.mathnet.ru/izv383}
\crossref{https://doi.org/10.4213/im383}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1918848}
\zmath{https://zbmath.org/?q=an:1053.14012}
\transl
\jour Izv. Math.
\yr 2002
\vol 66
\issue 2
\pages 393--424
\crossref{https://doi.org/10.1070/IM2002v066n02ABEH000383}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-33748499847}


Linking options:
  • http://mi.mathnet.ru/eng/izv383
  • https://doi.org/10.4213/im383
  • http://mi.mathnet.ru/eng/izv/v66/i2/p173

    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. 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
    2. O. V. Nikol'skaya, “On the geometry of a smooth model of a fibre product of families of K3 surfaces”, Sb. Math., 205:2 (2014), 269–276  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    3. O. V. Nikol'skaya, “On Algebraic Cohomology Classes on a Smooth Model of a Fiber Product of Families of K3 surfaces”, Math. Notes, 96:5 (2014), 745–752  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    4. 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
    5. 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 Российской академии наук. Серия математическая Izvestiya: Mathematics
    Number of views:
    This page:286
    Full text:87
    References:24
    First page:1

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2019