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Mosc. Math. J., 2015, Volume 15, Number 4, Pages 805–815 (Mi mmj588)  

This article is cited in 1 scientific paper (total in 1 paper)

On classification of groups of points on abelian varieties over finite fields

Sergey Rybakovabc

a Institute for information transmission problems of the Russian Academy of Sciences
b Poncelet laboratory (UMI 2615 of CNRS and Independent University of Moscow)
c AG Laboratory, HSE, 7 Vavilova str., Moscow, Russia, 117312

Abstract: In this paper we improve our previous results on classification of groups of points on abelian varieties over finite fields. The classification is given in terms of the Weil polynomial of abelian varieties in a given $k$-isogeny class over a finite field $k$.

Key words and phrases: abelian variety, the group of rational points, finite field, Newton polygon, Hodge polygon.

Funding Agency Grant Number
DST-1211005
Russian Foundation for Basic Research 12-01-31280
12-01-92697-IND-a
14-01-93108
Ministry of Education and Science of the Russian Federation
Supported in part by the research project DST-1211005, RFBR grants no. 12-01-31280, 12-01-92697-IND-a, 14-01-93108 and by a subsidy granted to the HSE by the Government of the Russian Federation for the implementation of the Global Competitiveness Program.


Full text: http://www.mathjournals.org/.../2015-015-004-014.html
References: PDF file   HTML file

Bibliographic databases:

Document Type: Article
MSC: 14K99, 14G05, 14G15
Received: April 2, 2014; in revised form October 17, 2015
Language: English

Citation: Sergey Rybakov, “On classification of groups of points on abelian varieties over finite fields”, Mosc. Math. J., 15:4 (2015), 805–815

Citation in format AMSBIB
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\by Sergey~Rybakov
\paper On classification of groups of points on abelian varieties over finite fields
\jour Mosc. Math.~J.
\yr 2015
\vol 15
\issue 4
\pages 805--815
\mathnet{http://mi.mathnet.ru/mmj588}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3438835}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000368530900014}


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    This publication is cited in the following articles:
    1. S. G. Vlăduţ, D. Yu. Nogin, M. A. Tsfasman, “Varieties over finite fields: quantitative theory”, Russian Math. Surveys, 73:2 (2018), 261–322  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
  • Moscow Mathematical Journal
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