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2010 | 8 | 2 | 282-288
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The groups of points on abelian varieties over finite fields

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Abstrakty
EN
Let A be an abelian variety with commutative endomorphism algebra over a finite field k. The k-isogeny class of A is uniquely determined by a Weil polynomial f A without multiple roots. We give a classification of the groups of k-rational points on varieties from this class in terms of Newton polygons of f A(1 − t).
Wydawca
Czasopismo
Rocznik
Tom
8
Numer
2
Strony
282-288
Opis fizyczny
Daty
wydano
2010-04-01
online
2010-04-14
Bibliografia
  • [1] Berthelot P., Ogus A., Notes on crystalline cohomology, Princeton University Press, Princeton, N.J., University of Tokyo Press, Tokyo, 1978
  • [2] Demazure M., Lectures on p-divisible groups, Lecture notes in mathematics 302, Springer-Verlag, Berlin, 1972
  • [3] Kedlaya K., p-adic differential equations, Cambridge University Press, to appear, web draft available at http://wwwmath.mit.edu/?kedlaya/papers/pde.pdf
  • [4] Rück H.-G., A note on elliptic curves over finite fields. Math. Comp. 1987, 49(179), 301–304 http://dx.doi.org/10.2307/2008268
  • [5] Schoof R., Nonsingular plane cubic curves over finite fields, J. Combin. Theory Ser. A, 1987, 46(2), 183–211 http://dx.doi.org/10.1016/0097-3165(87)90003-3
  • [6] Tsfasman M.A., The group of points of an elliptic curve over a finite field, Theory of numbers and its applications, Tbilisi, 1985, 286–287
  • [7] Tsfasman M., Vladut S., Nogin D., Algebraic geometric codes: basic notions, Mathematical Surveys and Monographs, 139, American Mathematical Society, Providence, RI, 2007
  • [8] Voloch J.F., A note on elliptic curves over finite fields, Bull. Soc. Math. France, 1988, 116(4), 455–458
  • [9] Waterhouse W., Abelian varieties over finite fields, Ann. scient. Éc. Norm. Sup., 1969, 4 serie 2, 521–560
  • [10] Waterhouse W., Milne J., Abelian varieties over finite fields, Proc. Sympos. Pure Math., Vol. XX, State Univ. New York, Stony Brook, N.Y., 1969, 53–64
  • [11] Xing Ch., The structure of the rational point groups of simple abelian varieties of dimension two over finite fields, Arch. Math., 1994, 63, 427–430 http://dx.doi.org/10.1007/BF01196672
  • [12] Xing Ch., On supersingular abelian varieties of dimension two over finite fields, Finite Fields Appl., 1996, 2(4), 407–421 http://dx.doi.org/10.1006/ffta.1996.0024
Typ dokumentu
Bibliografia
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bwmeta1.element.doi-10_2478_s11533-010-0003-x
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