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., 2008, Volume 72, Issue 4, Pages 197–224 (Mi izv753)  

On algebraic cycles on complex Abelian schemes over smooth projective curves

S. G. Tankeev

Vladimir State University

Abstract: If the Hodge conjecture holds for some generic (in the sense of Weil) geometric fibre $X_s$ of an Abelian scheme $\pi\colon X\to C$ over a smooth projective curve $C$, then numerical equivalence of algebraic cycles on $X$ coincides with homological equivalence. The Hodge conjecture for all complex Abelian varieties is equivalent to the standard conjecture $B(X)$ of Lefschetz type on the algebraicity of the Hodge operator $\ast$ for all Abelian schemes $\pi\colon X\to C$ over smooth projective curves. We investigate some properties of the Gauss–Manin connection and Hodge bundles associated with Abelian schemes over smooth projective curves, with applications to the conjectures of Hodge and Tate.

DOI: https://doi.org/10.4213/im753

Full text: PDF file (688 kB)
References: PDF file   HTML file

English version:
Izvestiya: Mathematics, 2008, 72:4, 817–844

Bibliographic databases:

UDC: 512.6
MSC: 14C25, 14D07, 11G20, 14K05
Received: 23.01.2006
Revised: 27.12.2006

Citation: S. G. Tankeev, “On algebraic cycles on complex Abelian schemes over smooth projective curves”, Izv. RAN. Ser. Mat., 72:4 (2008), 197–224; Izv. Math., 72:4 (2008), 817–844

Citation in format AMSBIB
\Bibitem{Tan08}
\by S.~G.~Tankeev
\paper On algebraic cycles on complex Abelian schemes over smooth projective curves
\jour Izv. RAN. Ser. Mat.
\yr 2008
\vol 72
\issue 4
\pages 197--224
\mathnet{http://mi.mathnet.ru/izv753}
\crossref{https://doi.org/10.4213/im753}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2452239}
\zmath{https://zbmath.org/?q=an:1157.14002}
\adsnasa{http://adsabs.harvard.edu/cgi-bin/bib_query?2008IzMat..72..817T}
\elib{http://elibrary.ru/item.asp?id=11161436}
\transl
\jour Izv. Math.
\yr 2008
\vol 72
\issue 4
\pages 817--844
\crossref{https://doi.org/10.1070/IM2008v072n04ABEH002417}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000259374600009}
\elib{http://elibrary.ru/item.asp?id=13584207}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-53349174165}


Linking options:
  • http://mi.mathnet.ru/eng/izv753
  • https://doi.org/10.4213/im753
  • http://mi.mathnet.ru/eng/izv/v72/i4/p197

    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
  • Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
    Number of views:
    This page:283
    Full text:75
    References:56
    First page:6

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