Izvestiya Rossiiskoi Akademii Nauk. Seriya Matematicheskaya
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., 1996, Volume 60, Issue 2, Pages 149–158 (Mi izv74)  

This article is cited in 3 scientific papers (total in 3 papers)

Hodge groups of abelian varieties with purely multiplicative reduction

A. Silverberga, Yu. G. Zarhinb

a Ohio State University
b Institute of Mathematical Problems of Biology, Russian Academy of Sciences

Abstract: The main result of the paper is that if $A$ is an abelian variety over a subfield $F$ of $\mathbf C$, and $A$ has purely multiplicative reduction at a discrete valuation of $F$, then the Hodge group of $A$ is semisimple. Further, we give necessary and sufficient conditions for the Hodge group to be semisimple. We obtain bounds on certain torsion subgroups for abelian varieties which do not have purely multiplicative reduction at a given discrete valuation, and therefore obtain bounds on torsion for abelian varieties, defined over number fields, whose Hodge groups are not semisimple.
Bibliography: 26 titles.

DOI: https://doi.org/10.4213/im74

Full text: PDF file (1118 kB)
References: PDF file   HTML file

English version:
Izvestiya: Mathematics, 1996, 60:2, 379–389

Bibliographic databases:

UDC: 513.6
MSC: Primary 14K15; Secondary 11G10
Received: 13.06.1995
Language:

Citation: A. Silverberg, Yu. G. Zarhin, “Hodge groups of abelian varieties with purely multiplicative reduction”, Izv. RAN. Ser. Mat., 60:2 (1996), 149–158; Izv. Math., 60:2 (1996), 379–389

Citation in format AMSBIB
\Bibitem{SilZar96}
\by A.~Silverberg, Yu.~G.~Zarhin
\paper Hodge groups of abelian varieties with purely multiplicative reduction
\jour Izv. RAN. Ser. Mat.
\yr 1996
\vol 60
\issue 2
\pages 149--158
\mathnet{http://mi.mathnet.ru/izv74}
\crossref{https://doi.org/10.4213/im74}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1399421}
\zmath{https://zbmath.org/?q=an:0904.14026}
\transl
\jour Izv. Math.
\yr 1996
\vol 60
\issue 2
\pages 379--389
\crossref{https://doi.org/10.1070/IM1996v060n02ABEH000074}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1996VL85500006}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-33645646832}


Linking options:
  • http://mi.mathnet.ru/eng/izv74
  • https://doi.org/10.4213/im74
  • http://mi.mathnet.ru/eng/izv/v60/i2/p149

    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. Zarhin Y.G., “Torsion of abelian varieties, Weil classes and cyclotomic extensions”, Mathematical Proceedings of the Cambridge Philosophical Society, 126:Part 1 (1999), 1–15  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus  scopus
    2. S. G. Tankeev, “On the numerical equivalence of algebraic cycles on potentially simple Abelian schemes of prime relative dimension”, Izv. Math., 69:1 (2005), 143–162  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    3. Orr M., “Lower Bounds For Ranks of Mumford-Tate Groups”, Bull. Soc. Math. Fr., 143:2 (2015), 229–246  crossref  mathscinet  zmath  isi  scopus
  • Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
    Number of views:
    This page:256
    Full text:131
    References:36
    First page:1

     
    Contact us:
     Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2021