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Izv. Akad. Nauk SSSR Ser. Mat., 1980, Volume 44, Issue 4, Pages 782–804 (Mi izv1843)  

This article is cited in 10 scientific papers (total in 10 papers)

Points of finite order on an Abelian variety

F. A. Bogomolov


Abstract: In this paper it is shown that the image of the Galois group under an $l$-adic representation in the Tate module of an Abelian variety has an algebraic Lie algebra which contains the scalar matrices as a subalgebra (Serre's conjecture). This paper also proves the finiteness of the intersection of a subgroup of an Abelian variety all of whose elements have order equal to a power of a fixed number with a wide class of subvarieties.
Bibliography: 13 titles.

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English version:
Mathematics of the USSR-Izvestiya, 1981, 17:1, 55–72

Bibliographic databases:

UDC: 513.6
MSC: Primary 14K05; Secondary 14M10
Received: 22.01.1980

Citation: F. A. Bogomolov, “Points of finite order on an Abelian variety”, Izv. Akad. Nauk SSSR Ser. Mat., 44:4 (1980), 782–804; Math. USSR-Izv., 17:1 (1981), 55–72

Citation in format AMSBIB
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\by F.~A.~Bogomolov
\paper Points of finite order on an Abelian variety
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1980
\vol 44
\issue 4
\pages 782--804
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\mathscinet{http://www.ams.org/mathscinet-getitem?mr=587337}
\zmath{https://zbmath.org/?q=an:0466.14015|0453.14018}
\transl
\jour Math. USSR-Izv.
\yr 1981
\vol 17
\issue 1
\pages 55--72
\crossref{https://doi.org/10.1070/IM1981v017n01ABEH001329}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1981MW12300002}


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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, “Cycles on simple Abelian varieties of prime dimension over number fields”, Math. USSR-Izv., 31:3 (1988), 527–540  mathnet  crossref  mathscinet  zmath
    2. S. G. Tankeev, “K3 surfaces over number fields and $l$-adic representations”, Math. USSR-Izv., 33:3 (1989), 575–595  mathnet  crossref  mathscinet  zmath
    3. Yu. G. Zarhin, “Torsion and endomorphisms of Abelian varieties over infinite extensions of number fields”, Math. USSR-Izv., 38:3 (1992), 647–657  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    4. Masami FUJIMORI, “Integral and rational points on algebraic curves of certain types and their Jacobian varieties over number fields”, Tohoku Math Publ, 4:4 (1997), 1  crossref  mathscinet  zmath
    5. Takashi Ichikawa, “Heights on a subvariety of an abelian variety”, Journal of Number Theory, 104:1 (2004), 170  crossref
    6. Wulf-Dieter Geyer, Moshe Jarden, “Torsion of abelian varieties over large algebraic fields”, Finite Fields and Their Applications, 11:1 (2005), 123  crossref
    7. Walter Gubler, “The Bogomolov conjecture for totally degenerate abelian varieties”, Invent math, 169:2 (2007), 377  crossref  mathscinet  zmath  isi
    8. Răzvan Liţcanu, “Petits points et conjecture de Bogomolov”, Expositiones Mathematicae, 25:1 (2007), 37  crossref
    9. Yu. G. Zarhin, “Endomorphisms of Abelian varieties, cyclotomic extensions and Lie algebras”, Sb. Math., 201:12 (2010), 1801–1810  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    10. 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
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