Nous estimons la fraction des classes d’isogénie des variétés abeliennes sur un corps fini qui possèdent un polynôme caractéristique donné modulo . Comme application nous trouvons la proportion des classes d’isogénie des variétés abeliennes qui possèdent un point rationnel d’ordre .
We estimate the fraction of isogeny classes of abelian varieties over a finite field which have a given characteristic polynomial modulo . As an application we find the proportion of isogeny classes of abelian varieties with a rational point of order .
@article{JTNB_2004__16_1_173_0,
author = {Holden, Joshua},
title = {Abelian varieties over finite fields with a specified characteristic polynomial modulo $\ell $},
journal = {Journal de th\'eorie des nombres de Bordeaux},
pages = {173--178},
publisher = {Universit\'e Bordeaux 1},
volume = {16},
number = {1},
year = {2004},
doi = {10.5802/jtnb.439},
zbl = {02184637},
mrnumber = {2145578},
language = {en},
url = {http://www.numdam.org/articles/10.5802/jtnb.439/}
}
TY - JOUR AU - Holden, Joshua TI - Abelian varieties over finite fields with a specified characteristic polynomial modulo $\ell $ JO - Journal de théorie des nombres de Bordeaux PY - 2004 SP - 173 EP - 178 VL - 16 IS - 1 PB - Université Bordeaux 1 UR - http://www.numdam.org/articles/10.5802/jtnb.439/ DO - 10.5802/jtnb.439 LA - en ID - JTNB_2004__16_1_173_0 ER -
%0 Journal Article %A Holden, Joshua %T Abelian varieties over finite fields with a specified characteristic polynomial modulo $\ell $ %J Journal de théorie des nombres de Bordeaux %D 2004 %P 173-178 %V 16 %N 1 %I Université Bordeaux 1 %U http://www.numdam.org/articles/10.5802/jtnb.439/ %R 10.5802/jtnb.439 %G en %F JTNB_2004__16_1_173_0
Holden, Joshua. Abelian varieties over finite fields with a specified characteristic polynomial modulo $\ell $. Journal de théorie des nombres de Bordeaux, Tome 16 (2004) no. 1, pp. 173-178. doi : 10.5802/jtnb.439. http://www.numdam.org/articles/10.5802/jtnb.439/
[1] Jeffrey D. Achter and Joshua Holden, Notes on an analogue of the Fontaine-Mazur conjecture. J. Théor. Nombres Bordeaux 15 no.3 (2003), 627–637. | Numdam | MR | Zbl
[2] Stephen A. DiPippo and Everett W. Howe, Real polynomials with all roots on the unit circle and abelian varieties over finite fields. J. Number Theory 73 (1998), 426–450. | MR | Zbl
[3] Gerhard Frey, Ernst Kani and Helmut Völklein, Curves with infinite -rational geometric fundamental group. In Helmut Völklein, David Harbater, Peter Müller and J. G. Thompson, editors, Aspects of Galois theory (Gainesville, FL, 1996), volume 256 of London Mathematical Society Lecture Note Series, 85–118. Cambridge Univ. Press, 1999. | MR | Zbl
[4] Joshua Holden, On the Fontaine-Mazur Conjecture for number fields and an analogue for function fields. J. Number Theory 81 (2000), 16–47. | MR | Zbl
[5] Y. Ihara, On unramified extensions of function fields over finite fields. In Y. Ihara, editor, Galois Groups and Their Representations, volume 2 of Adv. Studies in Pure Math. 89–97. North-Holland, 1983. | MR | Zbl
Cité par Sources :
